Thanks for your confirmation of what I already suspected.
However, removing dwprot was not easy as it was a selfprotected remaining file with associated undeletable registry entries after removing Dr Web "normally". I searched the web and found a lot of "solutions", oftenly including the download of "magic" removers or deinstallers. But none worked.
For those who might be interested, here is how I finally solved the problem. The solution could probably also apply for similar problems where files or registry entries can't apparently be deleted.
To remove dwprot.sys (located in C:\Windows\system32\drivers), I just booted from an Ubuntu CD (without install) and simply deleted the file. That worked, thanks Linux !
To remove the registry entries, I ran PsExec from Sysinternals, with parameters -i -d -s, which allows to delete locked entries. I then deleted all dwprot entries.
Finally I reinstalled Avast 7 and my system is now running for several hours without a single BSOD (before removing dwprot, I coudn't use the system for more than 1 or 2 minutes).