The avast icon is just and interface to the on-access providers and they should still be running check the Task Manager the avast processes are ashServ.exe (main scanning engine), ashMaiSv.exe (avast email scanner if you have it enabled), ashWebSv.exe (avast web shield, also if you have it enabled) and aswUpdSv.exe (the avast Update service), are these running ?
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. ?
What Operating System are you using ?
Whatever is stopping the avast icon from running would appear to be doing the same with your re-creation of the Run registry key. 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).