OK, it took me a while to get back to this, but here's where we are. We still have no solution.
I tried everything on the checklist
that you pointed me to. I downloaded a new raspbian wheezy image, verified the sha1sum, then reimaged the SD card. Verified that the card has two partitions, and the first partition has bootcode.bin, loader.bin, start.elf, etc.
I boot the Pi. The red light comes on, the green light flashes once and then stops. Still no HDMI signal.
Next I tried replacing bootcode.bin, as the checklist suggests. This time the green LED flashes 3 times, waits, and then repeats. Still no HDMI. According to the checklist, that means the Pi can't find either loader.bin or start.elf, but probably it just means that the replacement bootcode.bin doesn't work.
I don't have any component video devices to test with. I've tried connecting the Pi to our LAN, but my router didn't detect any new device on the network.
So at this point, I still have a dead Pi. It's never worked since we got it. Can you suggest other troubleshooting steps?