MSI motherboard beeps three times and doesn't boot

Solution 1:

Please see Why does my computer beep when I turn it on? What are these beep codes?

It indicates you have bad memory

AMI BIOS:
1 beep - System boot successfull
*1beep - Refresh failure - (NO VIDEO) memory refresh failure (bad memory)
2 beeps - Parity error - bad memory
3 beeps - Base 64K memory failure - bad memory
4 beeps - Timer not operational - bad motherboard
5 beeps - Processor error - bad processor
6 beeps - 8042 gate A20 failure - bad cpu or mainboard
7 beeps - Processor exception interput error - bad processor
8 beeps - Display memory read/write failure - bad video card or memory
9 beeps - ROM checksum error - bad BIOS
10 beeps - CMOS shutdown register read/write error - bad motherboard
11 beeps - Cache memory bad - bad CPU or motherboard
12 beeps - BIOS rom file incorrect size - The BIOS ROM file found does not match the size of the flash device
13 beeps - BIOS rom image mismatch - The BIOS ROM file layout configuration does not match image present in the flash device
5 short + 1 long beeps - Memory error - No memory detected in the memory slots.
6 short + 1 long beeps - Memory error - EDO memory detected in system
7 short + 1 long beeps - SMBUS error

Source

Depending on how much RAM you have in the PC, you have a few options:

If you have 1 stick of RAM, replace it!

If you have more, than remove all but one, see if the machine boots. Then, turn off the computer, use a different RAM stick and turn on the machine. Repeat until you find the dead/duff stick (assuming it's the RAM, and not the slot etc).

Also, just ensuring it's seated correctly could be of help

Solution 2:

In the manual I can see it has an American Megatrends BIOS (AMI bios):

MSI h61m-e23 Support

It seems you have a RAM issue: http://www.bioscentral.com/beepcodes/amibeep.htm