First you have been able to log in to the avast forum, which presumably will have been linked to that old email address ?
It is never wise to publish an email address in a public forum.
If this is correct then got to your my.avast.com account and log on, one logged on you should be able to add a new email address, once this new email address is confirmed, you can then select it as your primary email address.
In the top right of the my.avast.com page there is a portrait icon, click that and select My Profile. Now select the Email Management and now the +Add another email.