Welcome to the forum
When you say "not reading anything" - you're talking about all optical media i.e. CD/CDR/Audio CD, and both burned and pressed DVD discs?
If that is the case, have you tried using the cable that you were using in the old PC, or if you are already using the same cable, try a fresh one? Maybe double-check all cables are plugged in securely, too.
Can you boot from your Vista disc? You may have to change the boot sequence in your PC's BIOS to test this out.
I would doubt the drive itself has gone bad, between simply swapping it from one PC to another, although with computers anything is possible.