What other security software do they have installed (firewall, anti-spyware, etc.) ?
What Operating System is he using ?
Some have been known to block the avastUI.exe (a user startup item), which places the Icon and acts as the avast! user interface to the program/shield settings.
Whilst the tray icon and interface aren't directly related to avast protection, it makes you wonder if something else isn't right. The use of System Restore often screws up avast, so it isn't an ideal situation; you/he should disable the avast self-defence module before using it, that would be a problem since avastUI.exe isn't running.
He can find the C:\Program Files\AVAST Software\Avast\AvastUI.exe to manually launch the UI and place the icon in the tray, what happens if he double clicks on this file ?