I have a radeon 9800, and only a 250W psu.
My computer works. But if I turn it off, and then turn it on again some time later, the POST screen never comes on. Either I get a blank screen or a screen with red text that says my ATI needs to be connected to a power source (hdd style power cable).
At first, I thought this was a connection issue. I would open the box, wiggle the board, wiggle the power cable. Switch the power cables... and after a certain mysterious combination, it would work. And no problems then on.
Then one day, I turned on my computer, and I had to do something. It just sat there with a black screen. I came back and restarted it and it just worked.
That is when I think I understood what the problem is: I say it must be a capacitor the doesn't fill up fast enough on initial boot that makes the card think that it's not connected to a power source. But if you leave it on for a few minutes to 'warm up', it just works. Of course, the fiddling around masked the fact that it was staying on for that crucial amount of time, and made me think that the voodoo was that.
It's still all conjecture, but yeah, that's my voodoo.