Have (or did) you another AV installed in this system, if so what was it and how did you get rid of it ?

The little red warning over the “a” on the system tray is usually associated with the presence of or remnants of another AV, if avast detects this it can disable elements to avoid a conflict with the other AV.

Try a repair of avast. Add Remove programs, select ‘avast! Anti-Virus,’ click the Change/Remove button and scroll down to Repair, click next and follow. You need to be on-line to do this. Though I don’t think this will change much since you have even reinstalled avast.