Windows 7: Underperforming GTX 560

I want to know the culprit behind my newly purchased but underperforming Asus GTX 560.

I can play Resident Evil 5, Dead Space 2 and Warcraft III DOTA on highest settings without problems. But when playing NBA 2k12, COD Black Ops/Modern Warfare my system lags and gets just 7 FPS (26 FPS max during the night and wee hours).

My system consists of the following:
Intel Core i5 760
4GB (2x2GB) DDR3 RAM
CoolerMaster EX 500w

I have decided to buy a 600w CPU (an AeroCool Strike X 80PLUS Bronze maybe). But before that, I really wanted to know if it is really the PSU that's causing this problem, or the i5 processor? I have a very limited budget so I want to get the right component as much as possible.

To help you analyze the situation, here's a brief history of what happened:
I had a GTS250 before. All my games ran very, very well without lags on high settings. One day, while playing NBA 2k11, framerate suddenly dropped to 7 or 6 FPS. Sometimes it would return to normal but most times it would lag. Same problem on Call of Duty MW and Black Ops. I shrugged it off because I could play Dead Space 2 smoothly! So I thought it was just a Windows 7 problem. So I reformatted my drive and reinstalled 7. Nothing has changed. But this time I also got occasional BSOD during stratups and sudden shutdowns. So I thought my videocard is causing the problem so I bought an Asus GTX 560. Now, only the sudden shutdowns and BSOD's disappeared. Playing games are still a problem.

What are your thoughts? I haven't played since September and I'm itching so much right now. PSU or CPU? Or is it the motherboard? Please help.

Let me guess, you connected only one 6 pin connector to 560? That's why shutdowns disappeared. Card does not run at full speed. Connect the second one and watch shutdowns reappear. And then get new PSU

I'd try running memtest, to see if your ram is fudged

Also uploading the dump files from your bsod would help us determine the cause

I have both 6pins connected. One 6pin connector that directly goes from the PSU and the other 6-pin to 2 4-pin molex that came with the video card.

We don't know which ASUS 560 you have, but here is a power draw test for one of them. I think you are under-powered but can't say whether or not more power would help you. ASUS GeForce GTX 560 DirectCU II TOP Video Card Review - Power Consumption - Legit Reviews

My card's GTX560 DirectCU. Didn't see any "II" in the label. So if you think I'm underpowered but couldn't say whether more power or not would solve it, what other solutions are there?

I'm going to test Memtest when I get home today. Crossing my fingers... I'll update you guys. Thanks a lot!

I forgot to mention to check your PSU label to see what the max +12V amp and watts are and then check the chart I linked to see if it puts out enough.
Also you might see which nVIDIA driver you have, some recent ones have been buggy. The 270.61 and 285.62 have been the most stable.
Latest NVIDIA ForceWare Video Drivers Windows 7