Sorry, it was a bit of clutching at straws as there aren't many things to suggest relating to the try icon animation.
You mentioned files are being scanned, is this where you are checking that from the avastUI, Real-Time Shields, File System Shield, the shield traffic and Files scanned/infected:, Last file scanned: values should give an indication.
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.
Do you have any windows themes, etc. that might have any impact on tray icons, etc. ?