Go into the BIOS and make sure it's recognized the hard drive. Some BIOS's need to hunt for the drive manually. Make sure it sees it. Are you hearing any beeps? Usually, one beep means everything's OK. Multiple beeps of any kind indicate a problem, and it's different for each type of BIOS.
Sometimes, when a power supply fails, it takes other hardware with it, like memory, or a CD-Rom. Often, a computer won't start because of something like bad memory or a bad drive. Disconnecting the drive will allow the computer to boot. If the computer won't boot with the drive in it, the drive/memory/whatever will have to be replaced.
You can check the memory with a homemade CD of Memtest 86
or Microsoft Memory Checker
after the computer is booting. The computer can be booted from the disk and does not require the operating system. Bad memory may allow the computer to run, but will cause errors which can even mess up the hard drive.
The usual method of finding a bad part is to disconnect everything except what's necessary to run - video, motherboard, hard drive, memory, then try booting, then connect one thing at a time. I've personally had better luck removing one thing at a time, but of course, that wouldn't work if there was more than one bad part.