system
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I found the answer to the issue at techguy.org, the tech support forum I use 90% of the time when I have a technical issue. Turns out something (??) changed the permissions for the System Volume Information folder, removing me as having permission to open it. I had to use Safe Mode to access the Security tab under Folder Options to change the permissions to “Everyone”, but that solved the problem; Avast! now scans that folder and I get no “Some files could not be scanned” messages.
Thanks to all who contributed to this now solved issue.