If this is the icon, see image, then avast is scanning email.
If you aren't checking for email or sending email then you would appear to have an undetected trojan spambot.
If you haven't already got this software (freeware), download, install, update and run it, preferably in safe mode.
1. If using winXP
AVG anti-spyware (formerly Ewido) Resident scanner during trial On-Demand after trial ends. Or
SUPERantispyware On-Demand only in free version. Or
Spyware Terminator Resident scanner. Or
a-Squared free On-Demand only with free version(if using win98/ME).
Bearing in mind your missing avast 'a' icon this may be a little more than that, perhaps not. What you have done is a work around and isn't discovering why it is gone.
avast! icon missing - As a temporary measure until this is resolved 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). Right click on the file and select Send To, Desktop (create shortcut). You will need to run this after each boot until the problem is resolved.
What other security based software do you have that might block new startup entries, e.g. Spybot S&D (TeaTimer), AdAware (AdWatch), SpySweeper, Spyware Doctor (StartUpGuard or OnGuard), PrevX, WinPatrol, ProcessGuard, etc. ?
Check the option in the Appearance tab of Program Settings. Or Make a link to ashdisp.exe in your startup folder.