Without the GPU, I was able to log into Windows and install the chipset drivers. Computer works perfectly without the video card, but...
If I install the video card, I get the same problem, no power. I tried with my older GTS 250 video card installed, and it worked!
I did have trouble getting the 4+4 power cable inserted on the Radeon card. I wonder if something went wrong or broke there. Or, am I inserting the wrong power cable? The Radeon card has an 8 pin and 6 pin connection. I've been inserting the second 4+4 cable from the PSU, it's the same as the CPU power plug. Should I be using one of the modular 6+2 cables in the 8 pin slot?