The problem is definitely caused by avast! If you register C:\Windows\system32\taskmgr.exe as an exception in Behaviour Shield, the problem goes away and Task Manager works again.
But it can get worse! I have been in the situation where all I get after logon is a black screen, instead of the Start screen. I found that if I use Task Manager to start C:\Windows\explorer.exe, the screen comes back and it all works again! Again, the way to solve this problem is to specify explorer.exe as an exception in Behaviour Shield!
Note that it may be necessary to go into Services from Task Manager and stop the avast! service temporarily while you get things sorted out.
As I don't know what other executables avast! may be taking exception to, I am abandoning it in favour of Norton.