What other security applications do you have installed ?

Have (or did) you another Anti-Virus installed in this system, if so what was it and how did you get rid of it ?

There should have been dump files created during the BSOD, if you can send them to avast for analysis.

Upload them to ftp://ftp.avast.com/incoming - Using Internet Explorer, 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 zip file you are uploading a unique name (Cipro_memory_dmp.zip, etc.), so they can identify it. It might not be a bad idea to create a text file (readme.txt) with any relevant information, this avast topic URL, user name, etc. etc. in the zip file.
How to upload it using the Run command-line in Windows: Windows Key + R (to get the run box), copy and paste this

explorer ftp://ftp.avast.com/incoming

and drag the file into the window, from another explorer window.