There is no way that your graphics card is being properly powered. First of all, it requires a 6-pin PCI-E power connector, but you say no cords are plugged into the card. Even if you plugged in the 6-pin PCI-E power connector (if your power supply even has one), there is no way it would provide enough +12V amperage. Even if all 300W were dedicated to the +12V rail, and even if no other devices were drawing off the +12V rail, you would only get 25 amps of current (300 / 12), and more realistically, the power supply probably provides ~15 amps on the +12V rail. However, the 8800GT requires 30 amps, so you definitely need a new power supply.
The PSU you linked to (the BFG GS-550) would do, but my favorite sub-$50 PSU is this 450W Corsair
. While it has a lower rated maximum output, it actually has more amperage on the +12V rail (33 amps), which is what 90% of your system (including the graphics card) uses.