Mysterious boot problem

I have a problem that no amount of Googling or asking friends has helped.

When I try to boot my PC my fans come on as usual, but that's it, it doesn't boot. However I can boot from a live CD if my external HD isn't plugged in.

Then, when it is booted from the live CD, my internal HD is accessible as usual, and if I reboot I can boot from it as usual, but again, not if my external hard drive is plugged in.

Any ideas as to what the problem could be?

If you have more than one internal hard drive, unplug all but the boot drive and see if it helps. If you have a fairly modern graphics card, take it out of the system, use the on board graphics chip instead (if you have one) and see if it helps. So try to reduce the overall power consumption and see what happens.

Of course, if you have a more powerful PSU lying around, why not try that.

If all that doesn't help, it's likely another problem.