I would recommend uninstalling iTunes with Revo Uninstaller first to remove all related files. Then reinstall itunes and download the 3.1.2 software (you shouldn't have to pay since it's already associated with your AppleId.

Because you've done restores already, it seems like the 3.1.2 software you have on your computer or your itunes software or both are missing files or contain corrupted files.

This will basically reset your iphone. If you don't want to try that, you could try removing your old iphone software on your computer and redownloading the 3.1.2 software first. If that doesn't work, I would go all out and use Revo Uninstaller to remove all of your corrupt files.