My XP machine bit the dust. I had my authorization on that machine. Is there a way to de-authorize that computer and authorize another?

Sure, if you have the original install disks. Simply install XP on another clean (empty) machine.

What do you mean though by 'bit the dust'? The Hard Drive and data on it may itself be fine and recoverable. Have you opened up machine?

Basic trouble shooting for me would be first check all cables, clean out the dust, etc. then next unplug and replug, attach all devices, including video cards and all peripherals.

Does the motherboard post when it boots up? Is the HD seen in the Bios?

And like Fumi said, If you have the original install disks (or maybe the box, packaging), it should have license key to install on new machine.

but if you are installing a new OS, you may want to upgrade it either Win7 or 8.

My issue is that the computer won't even pwer on. It's an Xp machine, so I'm probably going to replace it soom. I have a laptop with Vista, another with Win7, a tablet with WIn8, and a small laptop running 10.
When I tried to install Office on another machine, I got an error message.
It said I couldn't authorize because I've used all my authorizations.
So I need to know if I can de-authorize my old machine.
Just having the discs apparently doesn't mean squat.

You can't 'de-authorize' an Office installation. What the message means is that your copy of Office has already been installed on as many PCs as the licence allows. In that case, if you want to transfer the licence to a new PC, you will need to use telephone activation, rather than relying on on-line activation.

__________________
Cheers,
Paul Edstein
[Fmr MS MVP - Word]