2.5 external HDD issue

I have the SimpleTech - Signature Mini 320GB External Hard Drive Model: FS-U25/320H. It has a 2.5 SATA HD inside. I am using Win XP Pro SP2.
The Product Features are as follows:

* 320GB maximum storage capacity
* High-speed USB 2.0 interface; USB-powered, so an AC adapter is not required for most computers
* Up to 480 Mbps data transfer rate for quick transfer of all your important programs and files
* 8MB cache buffer
* 5400 rpm for fast read/write times
* 8 ms average seek/read time
* Preloaded one-click backup software allows you to quickly and easily back up and protect all your digital data
* Simple, automatic backups with Fabrik Local Backup; includes 2GB of Fabrik Ultimate Backup online (Internet connection required
* Compatible with PC and Mac.
Now I have two computers. I used to have this connected to computer one. When I used the drive to transfer files to another computer, it no longer would be recognized on computer one. Computer two picks it up with no problem and any other PC I tried it on picks it up. But for some reason computer one will not detect it anymore. The front and back USB ports.
Can anyone understand how and why this is happening and how I can fix this issue? Thanks.
Also let me add that I did plug in other devices to all the USB slots in computer one and they all work fine.