I am wondering if I can run either a Radeon 6850 or 6870 on my 400W Corsair PSU.
My current specs are: CPU i3 2100. HDD Samsung Spinpoint F3 1TB. 8gb ram.
A Corsair 400 W is a good enough PSU for cards upto Radeon HD 6870, but you have to use a 6 pin adapter cable. If you have the spare cable (normally comes with the card) you can use a Radeon 6870 or else a Radeon 6850 should be ok.
One of my systems has an OC'd Q9550, 4 GB RAM, a GTX260 - a card with similar power requirements to a 6870, a Gigabyte EP45-UD3P motherboard, 3 hard drives and an optical, and a Soundblaster card all powered by a Corsair 750TX.
Running 3 instances of Prime95 to load the CPU and 3DMark06 to load the GPU, it pulls 375 watts from the wall as measured by my Kill-a-Watt meter. Figuring 80% efficiency, the system pulls 300 watts from the PSU.