Three Monitors Hooked Up, but I Can Only Use Two?

Today I got a new Sapphire Radeon HD 4670. I've attached two monitors into the DVI and D-SUB ports and connected my TV into the HDMI port (so essentially three monitors are connected).

So far the card is working perfectly, except for one thing I don't understand. All three monitors show up as potential displays in the "Screen Resolution" menu (I'm running Windows 7 64-bit) but one of them is blacked out, meaning it won't let me use it. More accurately put, it will let me use any two of the three to display/extend my desktop, but not all of them. What could be the problem?

Here's a screenshot from my main display:

I read something on here about something you can buy called a DisplayPort. Would that solve this problem or is there a less costly way?

You can only connect 2 monitors at once on a Radeon HD 4000 series card. Starting with the 5000 series cards, you can connect 3+ monitors, but can only have a maximum of two devices connected via HDMI, DVI or VGA. A third and any additional monitors require using a DisplayPort, which is a port on the card. Your card likely doesn't have one; as such, you are limited to two monitors.

See this post on ATI Radeon Eyefinity - 3 monitors for information on using 3+ displays on a supported card. It looks like for the card you have though, you are limited to just two monitors, unfortunately. If it's not too late to return the card, you may want to get a 5000 series card instead if you must use three monitors.