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.