Try a repair of avast:
XP - Add Remove programs, select ‘avast! Anti-Virus,’ click the Change/Remove button and scroll down to Repair, click next and follow.

Vista, win7 - Control Panel, Programs & Features, uninstall a program, select ‘avast! Anti-Virus,’ click the Change/Remove button and scroll down to Repair, click next and follow.

You may need to reboot after the repair.

If that doesn’t work you could try:
It may just be the avastUI that isn’t running, as a temporary measure this is the C:\Program Files\AVAST Software\Avast\AvastUI.exe file, create a desktop shortcut.
Or
Creating your own startup entry, this is the info for my startup entry, see image.
Or
Do a reinstall of avast, left this as a last option as it is more hassle.