Your power supply is fine. Dual 16A rails are plenty of 12v power ... and the PCI-E auxiliary plug will be on a different rail than the primary ATX connection, so the card has plenty of available power.
The most telling statement in your question is this: "... The only other ATX PC I have access to is identical to this system and results are the same. " ==> Identical PC, same results ... so you either have a compatibility issue or simply a defective card.
... I scanned a couple of forums; and it seems the G92 GPU used in the 8800GT has a compatibility problem with Via chipsets. I suspect this is your problem (although user forums aren't always the most reliable source of technical info). Your experience certainly tends to confirm this. If it's not a budget-buster for you, the 8800GTX does not use the G92, and (according to the forum posts) works fine with Via chipset boards.
Alternatively, you could buy a Radeon 3870 which should give you close to the same level of performance without any compatibility issues [
http://www.newegg.com/Product/Product.aspx?Item=N82E16814102719 ]