The PSU is an 800W unit, more than enough for this card. The lines are dedicated, not through an adapter of any kind. I've tried running the machine with the hard drive disconnected, no difference, not a power issue I can see.
After flashing the BIOS I found I was able to get the onboard VGA working via BIOS settings, which oddly didn't work before. Here's something interesting: I can run the machine with the GT440 or the motherboard's onboard VGA by itself (the latter of which is how I'm running it now). However, when I connect the 6950 to the machine the onboard vga refuses to work, even if I leave the card unconnected to the monitor. This is getting bizarre.
UPDATE: I can hear Vista's startup tune behind the blank screen and the board's little 'hello' beep when it starts up. AFAIK the system is working, the card is somehopw refusing any output to the monitor, by itself or by the onboard vga.