http://www.ebay.com/itm/Dell-Optipl...819625?hash=item3abcb0ffe9:g:3GIAAOSwfZ1WacRO
Dell OptiPlex 790 with i5 2400 (3.1GHz quad), 4GB RAM 250GB HDD W7Pro64 installed) for $190. One note - you will have to remove the HDD cage to fit the video card in this case. A drill with long bits is your friend!
http://www.ebay.com/itm/Gigabyte-RA...532782?hash=item35fa797dee:g:GkAAAOSwT~9Wi~o~
Gigabyte 7970 GHz Edition for $153. I've seen similar cards go for $130-135 if you're a little patient and wait for it.
You'll need a new PSU, something in the 400-500W range from a reputable maker (Seasonic, Corsair, etc). Likely pick up new for like $30-40AR.
Total cost around $370, maybe $350 if you're willing to scour for deals. Very solid gaming build, far better than most anything else at this price range.
I'd suggest an upgrade to a cheap 120-250GB SSD and then the free upgrade to Windows 10.
I would avoid buying a 7970 from anyone on eBay selling 4+ of them. There is a very good chance that those cards have been running at 100% power 24/7 for the last three years. Definitely wouldn't pay $160 for it.