Floppy power connector, You may be able to harvest one from a old floppy drive or even try to re-solder that one(if its loosing contact there, if its on the psu end, you can find a molex to fdd connector on the net or check for another one of those, most psu's had 2 of those)
The card should not be able to boot(should display a message about not connecting the power cable and to look at the getting started page for info, and your pc speaker should beep at you) at all without that connected. So if it boots, your card may be on its way out.
I had that problem it drove me nuts and even switched psu out which helped for a few months till late spring then summer. I have my doubts about the molex to floppy but it might work. Try to position the power cable to ware it exerts force against the card but again band aid. Got tired and bought a 7800gs till I got tired of the board being slower than dirt and sold it all off. Not happy parting with either card but needed the money.