Acutally, you will find that the services are not running for Avast. It has nothing to do with RPC or other windows services would be failing. Are other programs failing or is it just Avast? Much of the other talk is a cop out. Manually start the services, there are four Avast services, and it will run temporarily. It will fail again. This is a known issue to users. There is no fix for this at this time.
How are set your avast! services?
Control Panel > Administrative Tools > Services
I suppose you have to have four avast! services:
C:\Program Files\Alwil Software\Avast4\ashServ.exe (avast! antivirus service)
C:\Program Files\Alwil Software\Avast4\ashUpdSv.exe (avast! Update Service)
C:\Program Files\Alwil Software\Avast4\ashWebSv.exe (avast! Web Scanner service)
C:\Program Files\Alwil Software\Avast4\ashMaiSv.exe (avast! e-Mail Scanner service)
The two first of them should be Automatic loaded and the two last Manually loaded.