If you really want to build a rig for mining, the cheapest way is with a FX-6100 or some other FX-series 6-core. Add to that, 4GB of RAM (512MB per thread is sufficient - 1GB is plenty for a lightweight Linux distro and a dedicated miner.. 6GB might be better if it's multipurpose). No hard drive needed - you can boot a Linux Live USB, run the whole OS on your RAM, use persistent storage on the USB if you need to save anything.
No special heatsink needed unless you overclock.
400W PSU is plenty, even with a mild overclock. I'd go with 500-550W because it's roughly the same price as a 400W.
Total should be sub-$400, even $300 is possible if you keep a strict budget. Most likely won't pay off. Over 50% of the total PTS have already been mined, difficulty went way up. ROI could take 8 months, easily.
GPU miner already exists.
It *might* exist, just like I might be a billionaire if I claim to be. Without proof, it's kind of a moot point. Even moreso when, assuming a GPU miner exists, nobody will release it to the public.
So, it doesn't help the original poster at all.