So I went home last night and got to work on the computer. I tried various combinations of unplugging a piece of hardware then trying to turn the computer on, etc, but no joy. I tried a similar approach with the main cable from the power supply to the motherboard, pulling it out, plugging it back in, trying to turn the computer on, no luck, try again, etc. Finally, the LED stopped blinking and the computer turned on and booted up and now seems to be working fine. So, in short, the computer is working, but I have a feeling there's something fundamentally wrong that will probably rear it's ugly head again soon. The most likely culprit is a broken/gay power supply.
Anyway, thanks again for the help.