Your registration will work for version 6.x too.
Simply go to http://www.avast.com/internet-security
and get the trial version.
Download that. Once downloaded, run the setup. When it finishes, reboot. You have 30 days to use it even without your registration.
When you are ready, look into your old email, the one you received with the registration.
You can use that registration in your new system, in your new installation of Avast.
If you don't have the email or the old registration / license files, post again and I'll give you more instructions. The old email is the easiest of the options to recover the license. In any case, the new installation of Avast will get to use your valid license, until the same original date of the original license you bought.