Very Nice system. with weak video (HD6670, $80).
"I don't know which graphic cards are compatible with my desktop. "
Just about anything stronger than the 6670 will work in your desktop, subject to power requirements, size of card and case cooling. Any reasonable card will work. Oh, you are interesting in an HD6990. That's not a reasonable card. (And it's gotten really hard to find, Toms' thinks that a sign the next gen cards are almost here so maybe you should wait a few months until Christmas time when they might choose to launch.)
"Will Radeon AMD HD 6990 fit in my desktop?" Power, size, cooling.
Power limit. You have 600 watts. The 6990 has a 375W TDP. The rest of your system (not overclocked) should peak around 150W. So 600 should be fine. If you overclock then you can use a huge amount of power and 600 will be too small. Anandtech overclocked a 6990 and "based on our data we’re confident the 6990 is pulling at least 500W". So either upgrade power or don't overclock. You can hurt things if the power supply is undersized.
http://www.anandtech.com/show/4209/amds-radeon-hd-6990-...
edit: missed this "By default, the Radeon HD 6990 runs an 830 MHz core clock at 1.12 V. Flip the switch next to the CrossFire connector, though, and both settings jump to 880 MHz and 1.175 V, respectively, upping the power ceiling to 450 W (clearly, those eight-pin connectors aren't limited to 150 W). " If you flip the switch then 600 watts doesn't cut it anymore. How could you have this card and not flip the switch ? fyi officially amd says "750W Watt or greater power supply with two 150W 8-pin PCI Express® power connectors"
Case. I'd give cyberpower a call or take out a ruler. Watch for clearance for existing cables that would have to go around the new card. The power cables plug in on top, not on the back of the card. 6990 is a 12" long card. It's a solid rectangle.
Case cooling. The 6990 dumps half of its hot air in the case. Thus the case gets another 150w internal heat source. Added fans are good. Air flow is always front in, blow thru the case, back out. You can go crazy with fans on the sides and top. See where your case has mounting points.
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Aside: There are card that are much stronger than the ($80) HD 6670 you currently have without going to the crazy end like a ($800) HD 6990. Suggest you take the games you play and google benchmark and frame rates to see if a slightly more mainstream card like the GeForce GTX 580 or HD 6970 2gb would do. See article
http://www.tomshardware.com/reviews/best-graphics-card,... You cannot use a SLI or a crossfire setupwith your MB. Any of the non-SLI, non-crossfire solutions should work.