Computer won't boot - which component?

Hello again all! This past week I assembled a new system (my third one - yay!). The specs are as follow:

Processor = Intel Core i7 930
Motherboard = Asus P6T
RAM = Corsair DDR3 1600 Mhz (3x2 GB)
Video = XFX Radeon 5950 1 GB DDR5
OS = Dual Boot Win XP / Win 7
Power Supply = 1000 W

I received all the components, put them together and installed Win XP and Win 7. I noticed that BIOS and Win 7 were both reading the RAM incorrectly, no matter how many or how few sticks I placed in but figured I would determine the cause of that after I had updated all my drivers, etc.

The next day the computer would not boot. The fans and lights would come on but there was no BIOS beep or image on the monitor. My first assumption was that maybe the RAM was faulty, since it had been being read with incorrect values, so I returned it and received new sticks. This did not change anything.

My next attempt at correction was to swap out the motherboard. I replaced it with an identical one and pushed the power switch in anticipation...and it booted up fine. My RAM was being read correctly and everything seemed to have worked out. I loaded up a game and attempted to play in windowed mode while running Core Temp to monitor temperatures. I had played for about 20 minutes when the computer died completely. The temperatures had not exceeded 45 C. I attempted to reboot but the only response were the fans making a clicking sound as if they were attempting to turn on but couldn't. No lights (except for the motherboard) lit up either.

Thinking now that it was the power supply, I replaced it with another 1000 W identical power supply I had on my older computer. Everything now lights up but there is no BIOS beep and the monitor has no image. I switched out the video card, just in case, but still nothing. Is it my processor perhaps? TigerDirect is lenient with returns, but I would like to get a professional opinion from here before I call them again. Thank you for any input at all.