In answer to your question, if you have malware, (virus, trojans, worms etc) there are usually symptoms such as web searches and addresses redirected, applications not working, error messages, popups on the desktop - often warning of a spyware infestation, noticeable computer slowdowns etc.
This doesn't seem to be the case with you, the Avast error appears to be the only problem, so it's likely you don't have (significant) malware.
If re-installing doesn't work, that's something we'll have to address next.
It's no problem offering this help, it's a hobby, and a way to help pay Alwil back for the use of this excellent software. It takes me maybe two to ten minutes to research stuff concerning the "average" problem, and another 2-5 minutes to collate it into a post.
The procedure posted above would probably take me about 20minutes to carry out; perhaps you should allow about an hour, because you'll be less certain, and wanting to check each step etc, maybe have a few questions. That's OK.
You'll be a semi-whiz when we've finished.
Now,
something worth checking first: have you registered your Avast Home?
Failure to do so will prevent it getting updates. Info and registration form
here.Registration is free, my experience is that it is totally safe to use your home email address when registering, and the key will be posted to you within 24hr, usually immediately.
Lack of registration should not in itself cause the error you're having, but it's worth checking.
If you haven't registered, do that first. When you get the key emailed (if you haven't yet) copy the license key (by highlighting only the key, and pressing control and c, then right-click the tray icon, select "about Avast", click "License key", place the cursor in the field provided, press control and v, then click OK.