@ poulabas
The win32k.sys is a windows system driver and would fall in line with the problem being either RAM or driver, so I would suggest you try that memory test Eddy gave the link for.
For some people an avast repair gets things back in sync, were there is an inconsistency in the reported VPS version of about avast and when you check for updates, etc. Try a repair of avast. Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and scroll down to Repair, click next and follow.
I'm still hoping for some input from one of the Alwil team as this is beyond anything I have experienced, they really would be the only one to dig deeper into this.
Usually they would ask for the minidump files created on the crash to be uploaded to the ftp server for analysis. We could try than and see if it sparks some action, though that source isn't monitored by default only when requested.
Upload them to
ftp://ftp.avast.com/incoming - Connect to the link and drag the file into the Right pane and drop it, that starts the upload, you don't have read access to this folder. Give the minidump.dmp file a unique name like poulabas-minidump.dmp so it couldn't be mixed with another minidump.dmp upload.