At bob3160 & Pondus.
The problem is that it isn't "Some files cannot be scanned by Avast Antivirus", but "I followed your instructions and after another full virus scan it still shows as incomplete - unable to scan all files."
Which would appear to be a program issue rather than single or a few files not being able to be scanned. That is why I suggested an Avast Repair as a first step.
@ FITZ
As suggested attach a screenshot it may give more information (but I have my doubts).
If you did a reboot after the repair, we may be looking at a clean reinstall of Avast.
Also have you recently installed any other security related software ?