While the portable hard drive is connected to a computer running Windows XP with Service Pack 2 installed, you can try the following:

If you are running the "Windows Classic: Theme:

Richt-Click on the "My Computer" icon on your Desktop.
Choose "Manage".

If nessasary, click the + next to "Storage" to expand it's options.
Choose "Disk Management".

Does your disk appear there?
You might have to scroll down some to see it.

(If it does)
You might need to reformat it.
To reformat it, right click on it and choose "Format", IIRC...
However, this will (most certianly) wipe the contents of the hard drive.

(If it does Not)
You have a problem.
It could be one or more of the following:
1) A Damaged USB or Firewire Cable. (Replace it)
2) The Hard Drive in the Portable Container is physically damaged. (Check Warranty)
3) The Power Supply for the Portable, be it the part that's outside, or the circuit board inside, is damaged. (Replace or warranty check)
4) Drivers! You might have forgotten to install USB or Firewire Drivers for your Motherboard.
5) Patches! You might need patches from Windows Update or the manafacturer of your motherboard.

This is all i can think of at this time, but if i can think of anything else, i'll be sure and post it.
=)

Edited to add:
If you don't want to take it outta the external case and connect it to an IDE or SATA connector on a motherboard to reformat it...
You can try messing with your BIOS and try to set up the "Boot From USB" or "Boot from external Device" (and set it's priority to come after booting from your OS HD) or the like.
Hopefully, this will help windows see it when you boot up the pc with it connected externally.