Depending on the performance of your system, cpu, ram and obviously OS (please tell us mor about your system), when booting avast is scanning certain opened/accessed files.
Desktop icons start out as plain ordinary shortcuts until the file containing the icon image is accesed and the image extracted. So if your system resources are stretched this delay might be more protracted than normal (without this scanning), it might appear that avast has taken over your icons but this is incorrect.
Ensure that only those applicationa that are essential are allowed to start on boot, check the standard shield is set to Normal (default) sencitivity, the higher the sensitivity the more files scanned.
What other security based software do you have that might block new startup entries, e.g. Spybot S&D (TeaTimer), AdAware (AdWatch), SpySweeper, PrevX, WinPatrol, ProcessGuard, etc. ?
avast! icon missing - 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). Right click on the file and select Send To, Desktop (create shortcut).