Yes, you would, but I don't think you need to uninstall PT3.
All you need to do is re-install postgres - this is completely separate from PT3.
As for your reg code - are you logged into the forum with the same user as you used when you bought PT3?
You can always re-request your reg code via the Support system if you can't see it on the forum, although you should be able to see it via My Account.