What do you mean the anti-virus doesn't work as the system tray icon isn't the avast protection but an interface to it ?
- Does the avast 'a' icon (when it does appear) have a red circle with a bar over the icon ?
- What avast processes are running in Task Manager, they begin with ash or asw, see image ?
- Have (or did) you another AV installed in this system, if so what was it and how did you get rid of it ?