The icons rotates giving an indication when files are scanned and avast is working. It is also the link to the On-Access scanners. It also allows you access to the right click context menu so you can adjust program settings, run on-demand scans, etc.
What other security based software do you have that might block new startup entries, e.g. Spybot S&D (TeaTimer), AdAware (AdWatch), PrevX, WinPatrol, ProcessGuard, etc. ?
As a temporary measure you can create a desktop shortcut for this file C:\Program Files\Alwil Software\Avast4\ashDisp.exe (the avast icon and interface to the providers).
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.
If that doesn't work try, uninstall, reboot, install, reboot.