Liek Dee says, you can get a cheap USB external caddy (5.25" version) which will accomodate the burner and let you use it completely independantly of the PC. Then when you get the PC fixed, you can just use the external drive on that too.
You should still be able to burn DVDs on a USB1.1 link, but don't be shocked if 2x or 4x is the fastest possible.
USB2.0 is 40x faster than USB1.0 !!!
(You can also get a PCMCIA USB2.0 card, which might go some way to solve the issue.. but depends how much you're wanting to spend :p)