First off, do you have avast set to scan while the screen saver is running?
Do you have a program like Norton Ghost, Goback, or the Windows Indexing service running?

If not, check your processes list (ctrl+alt+del) Do any of those show abnormal cpu usage? If so what is the process name.

Do you have abnormal network activity?

Awnsering any of this could help diagnose your problem.