|"..... I turn the computer off,...."|
You MUST REMOVE the AC power to the computer, not just have the computer not running, otherwise you can DAMAGE the card's circuits, or the PCI-E X16 slot's circuits, or both.
The video card DOES NOT require any software on the hard drive while booting the computer BEFORE the operating system is loading in order to produce video from it.
GeForce 9600 GT
Minimum System Power Requirement (W) 400W
Supplementary Power Connectors 6-pin
AMD Radeon™ HD 6770 Graphics
■450 Watt or greater power supply with one 75W 6-pin PCI Express® power connectors recommended (600 Watt and two 6-pin connectors for AMD CrossFireX™ technology in dual mode).
■Certified power supplies are recommended. Refer to http://ati.amd.com/certifiedPSU for a list of Certified products
(Dual mode = two HD 6770 cards, or two HD 6770 video chipsets on one card e.g. 6770 X2.)
If you have, say, a 350 watt PS, you might be able to get away with that capacity for the 9600 GT card, but not likely for the HD 6770 card.