You can install with the vista/XP cd on any system, but the key won't work except for the "original" system.
Once you reinstall and verify with the key code, you'll have to contact MS and convince them to allow you to move the OS to another system.
AW systems have (or used to have anyway...) the OS installed and activated with their OEM key at the factory, but once you reactivate the OS with the key from your system, the hardware is catalogued in MS's database. Next time you reload and try to activate, it checks your hardware. If it doesn't match, it won't activate the OS and you'll have to call MS to get a new key.
I had a system with a mobo replacement after I registered it, so I had to call MS every time I reinstalled. I got around that by just making an image of a fresh install with Norton Ghost with the OS activated. Load that and you won't have to go through that procedure again.
It is possible if AW is still using their OEM key to activate the OS for an AW system, to then use the disc on another machine, then register that machine with the key. You can then use respawn to reload on the original system or an image, and you may be able to use the key with another, but it's illegal and against the license terms for windows.
Once you register with MS with the OS key, any changes in hardware like upgrades will send a red flag. It's a pain in the butt.