You don't have to de-register it, you have a license for 3 systems, 2 active and 1 not active (on the broken laptop). So it is a cumulative active systems/installations.
When you renew your license for 3 systems, the new laptop can use the 3rd system license. The old laptop won't count as it isn't active.
The Avast subscription expires on the 22nd of November and I use all three licences, except I don't now as one laptop died a couple of months ago. The replacement laptop came with a trial version of McAfee running which is also due to expire soon.
What worries me is I remember getting an email from Avast when I registered the last computer telling me I had used two licences and had one remaining. To me it inferred the licence was tied to the individual device regardless of whether it was active or not.
I'll try and track down the email.
Thanks for the help.