hi steven_gpx,
Since the proposed PC replacement is for a new and different machine, you would lose the first license of the original three. You would need to use a second license to activate avast! on your new machine.
So, no, a license for a specific machine is not transferable.
You bring up an interesting point. Without a backup plan in place, you will lose all your personal files, which to me, is more important than losing the ability to run certain programs that are tied by licenses to the old computer that died?
Imaging software is available to back up your hard drive in case it should ever fail or even for cases where it gets infected with malware. Some of these programs are free and work just as well as paid.