What I would do considering your budget...
Processor:i7 2600K (sandybridge) all the way! The whole sandybridge series is a lot cheaper than the first generation of i3/i5/i7 processors, and IMO, far more performant.
Do not confound with the i7 2600, which is harder to OC. If you don't want to OverClock, take this one instead.
Heatsink: I'd go with a watercooling system, but if you don't plan on OCing, the heatsink that comes with the processor will do the job.
Motherboard: Any high-end Asus or Gigabyte motherboard with LGA1155 socket should do.
Make sure to take one with a P67 Chipset, because the H67 chipset makes it harder to OC.
Note that the P67 does not support the built-in "GPU" that is in the Sandybridge processors, but since you plan on building a gaming machine, you will most likely have a PCI-e 16X card.
I'd take a ASUS P8P67 WS Revolution or something equivalent. Please don't waste your money on MSI or ECS motherboards (not saying they are completely bad, but their components seem to be much more fragile).
Only downside about this motherboard is that it does not support triple channel memory.
I don't know much about Power supplies, but I'd go with one with over 700W and NOT made by OCZ.
Memory: Depends on how much memory you want, but considering the motherboard I suggest has only 4 slots, I'd go with any 1333MHz Corsair/Kingston/Mushkin kits of 2*4GB sticks.
Video card: I'd go with any 2GB DDR5 video card from XFX or Sapphire and if you want, you could try to get two copies of the same Graphics card and use them in SLI or CrossFire to get even more performance.
(note that the motherboard I suggested supports 3-way SLI and Quad CrossFire, so you could go even further but I think it's too expensive for nothing)
HDD: I'd go with a Caviar Black from Western Digital with SATA 6.0GB/s interface here. I don't know how much space you need, so it's up to you to decide how much capacity you want your HDD to have.
Don't forget to get a Blu-ray or DVD reader. I guess any brand will be good enough.
And for the OS, any Windows 7 64Bit as long as it is NOT Starter or Home Basic edition. I don't think it's worth it to get the Pro or Ultimate version of the OS, unless you want the Bitlocker feature (available only on Ultimate).
Note that Home Premium only supports up to 16GB of RAM, I doubt you will get higher than this though
Finally, take time to choose a good computer case with good airflow that supports ATX form factor motherboards.
Well, that's pretty much what I would do if I had such a budget. I didn't calculate how much this setup would cost you, but I have no fear you are still in your budget. Hope I helped you!