You are 'not' unprotected as you yourself have shown, everything else will work, just that your signatures won't be fully up to date.
What is the VPS version you have, right click the avast 'a' icon select about avast (the latest VPS is 000760-2) ?
You can try a manual update, right click the avast 'a' icon, select Updating, iAVS Update, does that work ?
Your registration key email should arrive within minutes, unless your ISP or your spam filter gets it, that is why I gave the email address so you can add it to any anti-spam whitelist/filter.
What is your ISP was that the email domain you are sending it to ?
If so you could try registering again using a different email address domain, if you haven't got another address try getting a free Yahoo email account address.