Hi,
Welcome to TSF.
Lets see if we can get the one installed on this PC up and running.
Do you "see" the CD-Rom in MY COMPUTER?
Are there any errors in the Device Manager (Yellow !)? If so please post them.
Have you uinstalled the CD-Rom Driver in the Device Manager, reboot and let XP reinstall the drivers?
This may also help:
http://support.microsoft.com/kb/314060/EN-US/
As far as an external CD-Rom it will make no difference if it is a laptop or PC.
I do believe though a new internal CD-Rom is cheaper than an external one.
Hope this helps,
Bill