Each time you re install GS 3 you must "re- register" unless you have the backup registration from the first time you installed it.
It's a simple text file you were asked if you wanted to save when you installed GS 3.
I have the backup registration file, and when I re-installed GS 3 the application said you have to register, but you can then choose the backuped redigstration file and it goes though as a valid key.
It all should go smooth as long as you have that file, burn it on cd and format your computer. Try first by uninstalling GS and using the backup file. (before formatting the whole computer)
I did a very similar thing, and tried to use the backed up registration, but it wouldn't accept it. I'm not sure what the backup registration is used for, but it didn't work for me. Anyway, I did an Internet based registration and that worked. GS3 generated a completely new registration key on the reinstall, but their Internet registration systems seemed to detect that it was being reinstalled on the same hardware and allowed the registration to go through.
I have restored the registration backup to a reformatted drive numerous times. It's never let me down.
Two ways to go:
1. Backup to the default location and copy that folder somewhere else
2. Manually make a folder on another drive and backup there
The backup files are hidden so you have to make sure you copy the folder containing them. Turn on View Hidden Files in Windows to make sure. Also, trying to muck with these files by changing the attributes to make them non-hidden will mess up the registration. Leave them as the are and copy the folder containing them.
You have to complete one registration process and back that up. Then when reinstalling to a clean drive, don't go past the first screen into another registration. From that first screen, restore the backed up registration.