Avast is bad about picking up false positives.

Some more advice from me...
1. If you're computers runs slowly, go to Start->Run (or win+r) and type in msconfig, then go over to the Startup Tab. Go through the list here and start deselecting things you don't need. Frequent items that slow down computers are adobe reader, quicktime, real player, and things like that. Most of these programs aren't needed on startup. Sure, they'll make it faster when you start up adobe reader, but they slow everything else down. However, don't deselect things if you don't know what you're doing! If you don't know what something is in startup, google it and do research!
2. If your browser is running slowly (or sometimes having problems with websites), try removing useless toolbars like Google and Yahoo toolbars. These are useless things which slow down your browser. Some things (like Blackboard) have problems if your browser has these toolbars as well, and since most browsers have their own search bar, these toolbars are pretty useless anyway. Also, if you have mywebsearch toolbar, remove it! It's spyware!
3. For slower computers, what you can try doing is having an antivirus program like AVG, but disabled the automated scan. Sure, Windows will probably complain, but as long as you run manual scans every so often and are smart, you'll probably be safe. I wouldn't recommend this to the average person, so make sure you're secure first!