In addition to John's suggestions:

- If you have more than one IDE port on the motherboard (which is most
likely), have you tried using the other IDE port?

- When trying the other IDE port, have you then tried disabling the
unused IDE port in the BIOS?

- There is usually a jumper on the motherboard (a 2-pin header) where
you can slide on a shunt that will clear out the BIOS. Tried that?

- Have you checked your BIOS settings, like that you are using AUTO for
drive detect and have enabled LBA?

- When you startup the computer with the "bad" hard drive in it, can you
hear the drive spin up just as you turn on power? If not, maybe the
female pins in the Molex connector are loose. You can (with power off)
stick in a tiny jeweler's screwdriver and carefully pinch the sides
(it's a tube with a split) so the split gets reduced and will grab
better the male pins on the hard drive. Or, for now, just try using a
different power connector. If you have a Y-adaptor, remove it and
connect the power connector from the power supply; it could be a crimp
got loose in the Y-adapter and the wire doesn't make a good connection
anymore.

Since the hard drive works in one machine and not in another, it's not a
problem with the hard drive. I would suspect power, cabling, or BIOS
problems, or maybe a bad IDE port. There is some common circuitry
between the IDE ports, so if everything else checks out okay but you
still cannot get the hard drive to work on the other IDE port, you could
try to buy an IDE port card. The problem with that is it is not the
primary IDE controller, so during Windows install you may have to press
F6 at the start to tell the setup program that it later has to ask you
for a driver in order to find the mass storage device (the setup handles
the secondary IDE controller like it is a SCSI device).