Pressing specific 3 buttons at a time not working but other 3 combinations are working [duplicate]

Whenever I play a PC game with the directional keys, I can only press two buttons at a time. For instance if I am playing a shooter like R-Type, I cannot hold down the fire button while moving diagonally at the same time. The computer simply ignores the extra button press.

How do I remove this limit so I can shoot while moving diagonally? This limitation seems to apply for every game.

I am running Windows 7 if it makes any difference. I noticed the same problem back when I used Windows XP.

This is a hardware limitation of your keyboard. Unfortunately, the only solution is that you must purchase a better keyboard that does not have this limitation.

To be more specific:

In order to save money, keyboard manufacturers often put many keys on the same "circuit" of sorts within the wiring of the keyboard. This prevents multiple keys in the same region of the keyboard from being pressed simultaneously. Sometimes it even prevents more than 2 keys at all from across the whole keyboard being pressed at once. Often the shift, ctrl, and alt keys are not within this limitation, so you can hold shift and press 2 other keys at once and it will still work fine.

Even high-end gaming keyboards often have a similar hardware limitation, although the cap is much higher so that it is unlikely to be reached during the normal course of gaming.

The keyboard enthusiasts forum at geekhack.org has an extensive list of keyboards (login required) tested for their N-Key-Rollover capabilities, as well as instructions on how to find the number of simultaneous keypresses a certain keyboard supports.

X-key-Rollover (where X is an integer smaller than the number of physical keys) is the minimum number of keys that will register correctly under any circumstances. True N-key-Rollover (NKRO) means that all keys can be held down and register correctly. Most standard keyboards offer only 2KRO, and although it is possible that certain key combinations allow more keys to register simultaneously, this is not guaranteed, and may differ even between different revisions of the same keyboard.

Here's a list of keyboards having a confirmed NKRO over a PS/2 connection or 6KRO/18KRO over USB (which is a USB limitation) from the geekhack.org forum thread (login required) (June 5th, 2012):

Adesso MKB-125B: 6KRO with USB cable adapter, NKRO with PS/2.
Adesso MKB-135B (full sized): 6KRO with USB cable adapter, NKRO with PS/2.
Cherry G80-3494 (Cherry Red): 6KRO with USB, NKRO with PS/2 adapter.
Cherry G80-3600 (Cherry Red): 6KRO with USB, NKRO with PS/2 adapter.
Cherry Corp G80-8200lpdus: NKRO PS/2.
Cherry G80-1950PQAXB.
Cherry Corp MX8100 G80-8113LRCUS-2: NKRO PS/2.
Cherry Corp G80-8113HRBUS-2: NKRO PS/2.
Cherry Ergoplus G80-5000HAMDE/03: NKRO PS/2.
Das S: 6KRO under USB, NKRO with PS/2 purple adapter.
Das 3 (previous model): 12KRO under USB, can not be used with PS/2.
Deck Legend: 6KRO under USB, NKRO under PS/2.
Deck 82 Key: 6KRO under USB (no PS/2 option).
DSI Modular Mac.
Ducky keyboards. 6KRO under USB, NKRO with PS/2 adapter.
Ducky G2 keyboards (special edition). 18KRO USB and NKRO PS/2.
F21-7d Mechanical Keyboard . 6KRO over USB (no PS/2 option).
Filco Keyboards Listed as NKRO. 6KRO under USB, NKRO with PS/2.
G-Tune Realforce 108B-MP - NKRO over PS/2.
IBM Model F AT: NKRO AT/PS/2 adapter.
iRocks KR-6230. 6KRO with USB.
KBC Poker. 6KRO with USB. NKRO with PS/2 adapter.
Key Tronic KB101 Plus: NKRO PS/2.
Kinesis Advantage: 6KRO under USB.
Kinesis Contoured: 6KRO under PS/2.
Leopold FC200R: 18KRO USB (Windows/OSX/Linux), NKRO with PS/2
Leopold FC500R (FullSize): 18KRO USB (Windows/OSX/Linux), NKRO with PS/2.
Marquardt MiniErgo: NKRO PS/2.
Matias Tactile Pro 3.0: 6KRO USB.
Microsoft Sidewinder X4: 18KRO over USB 
NCR Cherry G80-0528H/10 NKRO PS/2.
NEC APC-H412: NKRO PS/2.
Noppoo Chocolate Min (tenkeyless): Full NKRO under USB and NKRO PS/2.
Noppoo Chocolate Pro (fullsize): Full NKRO under USB and NKRO PS/2.
Northgate Omnikey 101 and CVT Avant Stellar: NKRO PS/2.
PFU Happy Hacking Keyboard: 6KRO under USB. Can not be used with
    PS/2 adapter. 
Qpad MK-80 (Cherry blue): 6KRO with USB, NKRO with PS/2 adapter
    (included).
Qpad MK-85 (Cherry red): 6KRO with USB. Can not be used with PS/2
    adapter.
Raptor Gaming K1: 6KRO under USB. Can not be used with PS/2 adapter.
Rosewill RK-9000 (Gen1, nonremovable cord): 6KRO USB, NKRO with PS/2
    adapter.
Rosewill RK-9000 (Gen2, removable cord): 6KRO USB, NKRO with included
    PS/2 cable.
Steelseries 6G Version 2, 7G: 6KRO USB, NKRO with PS/2 adapter.
Thermaltake Meka G1: 6KRO under USB, NKRO with adapter.
Topre Realforce: 6KRO under USB. Can not be used with PS/2 adapter.
XArmor U9BL: NKRO under native PS/2, 6KRO thru green USB adapter.
XArmor U9BL-S (Cherry Brown): 6KRO USB, NKRO with included PS/2 adapter.
Zenith ZKB-2: PS/2.

The following keyboards support only 2KRO and sometimes even fail to register common game-related keypresses (Source: geekhack.org forum thread (login required), June 5th, 2012):

Cherry Corp G80-3000 (all variations): 2KRO. Fails QWA.
Cherry Corp G80-8200HUAUS-2 (Note: USB Version): 2KRO
Cherry Corp G80-6421 (MX SPOS): 2KRO. Fails QWA.
Cherry Corp G80-MX-11900: 2KRO
Das 2 (Cherry Corp OEM) and Das 1 (Rubber Dome): 2KRO. Fails ASX.
Deck 82 Older Fire and Gold models.
Filco keyboards not specifically listed as NKRO: 2KRO
IBM Model M: 2KRO. Fails ASX, WDE, WAQ, and many others.
iOne Scorpius M10: 2KRO. Fails WASD.
Omnikey Evolution: 2KRO
Omnikey NCS: 2KRO. Fails QAS
Plum 87: 2KRO. Fails WDE, WAQ
Rapoo V7: 2KRO
Razer BlackWidow/BW Ultimate: 2KRO
SteelSeries 6Gv1: 2KRO. Fails QAS, WSD despite being advertised as 8KRO.
Tipro Matrix keypads/boards: 2KRO according to software documentation. 
TG3 BL82: 2KRO. Fails ASW.
Unicomp Customizer 104: 2KRO. Fails WDE, WAQ and many others.
Xarmor U9 - 2KRO - Fails WRV
Xarmor U9W - 2KRO - Fails ASX

"Gaming Optimized" keyboards try to support typical gaming-related key groups, often by giving left-hand keys priority over right-hand keys. Yet even these kinds of keyboards are mostly just 2KRO, and thus sometimes fail to support relevant key groups (Source: geekhack.org forum thread (login required), June 5th, 2012):

ABS M1: 2KRO - fails WAS, WDE, Caps-LShift-S
    (despite being advertised as 6KRO).
Deck Fire 82, Toxic 82, Gold 82 (since corrected in Deck Ice 82): 2KRO.
    Fails QWE.
iRocks KR6820: 2KRO but is optimized for many common gaming key combos.
Logitech G11 : 2KRO. Fails QA-Downarrow.
Logitech Gaming Keyboard G110: 2KRO Fails ZXC, MKL.
Logitech G15V1: 2KRO Fails Rshift-RightArrow-UpArrow,
    Rctrl-DownArrow-LeftArrow.
Logitech G15V2: 2KRO 
Logitech Illuminated Keyboard: 2KRO. Fails Lshift-W-Spacebar.
Microsoft Sidewinder X6 : 2KRO. Fails Ctrl-W-R.
Razer Black Widow (lighted and non-lighted): 2KRO. Fails ZXC.
    Well optimized around WASD/ESDF clusters. Any combo above 2 arrow keys
    fails (note CTRL-AQ does work), ESDF combo.
Razer Lycosa: 2KRO. Fails HJK but passes ASX.
Rosewill RK800G. 2KRO. Can press Q, W, E, A, S, D, space, up,
    left arrow, right arrow, down at the same time.
Saitek Eclipse: 2KRO. Fails QWA, LOP.
SteelSeries 6Gv1: 2KRO. Fails QAS, WSD despite being advertised as 8KRO.
SteelSeries Merc Stealth: 2KRO. Fails ERT, DFG, CVB despite being advertised
    as 7KRO. 

The other answers already do a good job at explaining why the limit cannot be raised. This answer will try and explain what the limit is and why it exists in the first place.

The reason why many keyboard won't allow more than 2 keys at the same time (with a few notable exceptions like Ctrl + Alt + Del), is because of a feature called "anti-ghosting".

What is anti-ghosting and why do I need it?

As the name implies, anti-ghosting is a feature meant to prevent ghosting, which is a bug that appears as soon as people attempt to press more than 2 keys simultaneously. As soon as the 3rd key is pressed, the keyboard will see a 4th (ghost) key being pressed.

How is ghosting even possible?

In the past, each key on a keyboard was attached to its own unique wire, so the keyboard knew exactly which keys were pressed. In order to reduce costs, manufacturers chose to reduce the amount of wires needed to map all keys. To do this, they created a grid and mapped the keys to the grid.

Consider the following keyboard: It's a simple keyboard with 9 keys (numbered 1 to 9) mapped on a grid, which uses 6 wires (instead of 9), 3 horizontal ones, and 3 vertical ones.

 | | |
-7-8-9
 | | |
-4-5-6
 | | |
-1-2-3

If I press key 7, the left column and top row will send a signal to the keyboard. The keyboard knows which key I pressed, because there is only 1 key mapped to both the left column and the top row.

If I press 8, the middle column will also fire, but since I haven't let go of 7, the left column is still lit up. At this point, the keyboard knows that I'm pressing 7 and 8 simultaneously, because those are the only possible keys that can light up both the left and middle columns, which are both mapped to the top row.

But what happens if I press 5 as well? At this point, the middle row will light up, but the keyboard has no idea which column the signal belongs to, since the left and middle columns are both being pressed right now. Because of this, the keyboard will assume that I not only pressed 5, but also 4 as well.

Key 4 is a "ghost key", because it appears as being pressed even though it's not. With anti-ghosting, the keyboard will ignore both 4 and 5, because it doesn't know which was pressed.

But I can press Ctrl + Alt + Del, no?

Yes. Depending on the mapping of the keys, it is possible for the keyboard to detect 3 or more keys simultaneously. Most manufacturers design their keyboard in such a way, that people can press multiple modifier keys (Shift, Ctrl, Alt) together with at least 1 additional regular key.

However, while this is good enough for most users, it's not enough for a gamer that needs to press W + A + Ctrl +          all at once, and another gamer might need a completely different combination of keys altogether.

So how do I know what keyboard I should buy?

Luckily, there's a term for it: "rollover".

While different keyboards may support different combinations of 3 or more keys, all of them are guaranteed to recognize at least 2 keys simultaneously. This is known as a 2-rollover, which means any 2 keys will be recognized.

Many gaming keyboards mention their rollover. Some may be advertised as 3-rollover (any 3 keys work) or 5-rollover, some high-end keyboards may even be 10-rollover (any combination of 10 keys are recognized). The most expensive keyboards may also be advertised as "n-rollover", which means that you can (in theory) press all keys on the keyboard at the same time, and they would all work.

The term may vary depending on the manufacturer or the store that sells them. For instance, I found a keyboard on Amazon that claims to have "19 Non-Conflict Keys", which likely refers to a 19-rollover.

Naturally, the higher the rollover, the more expensive the keyboard.

As a general rule-of-thumb, if the keyboard is not aimed at gamers, chances are it's only 2-rollover and therefore suffers from the same 2-key restriction. Be careful, though! Not all gaming keyboards are guaranteed to be 3-rollover or higher; some may simply be optimized for WASD despite being only 2-rollover. If you want to avoid any surprises, pay attention to the keyboard's rollover.

If there is ever enough demand for it, simultaneous keypress support may become a standard stat available, but that is not likely.

I have heard that the SteelSeries Zboard supports many (7 I think) kepresses. Another I have heard is Avant stellar. This discussion might also interest you.