Normally you just uninstall on the one system and install on the other.

Since the computer is dead, you probably aren’t going to be able to uninstall it. So just proceed with the installation on the new system, if you saved the license file (license.avastlic) transfer it to the new system and action it as you did before.

If you don’t have a copy of the license file - you can use the - Resend avast License http://www.avast.com/resend-license-paid.php, you will need to enter the email that you used when purchasing the license, e.g. the one that the original email with the link was sent.