I have Nvidia cards in the systems with my 4797 events. Glad you found a fix for your issue, but it sounds like it's not the same issue. Also, I didn't see you mention if you have Windows 8 or not. If you are not running Windows 8, then you certainly did not have the same issue as Event ID 4797 "An attempt was made to query the existence of a blank password for an account." is new and unique to Windows 8 and is not in Windows 7 and lower. (not speaking of Server OSes).
I also get Events 4624 4634 4672.
I have uninstalled Avast from another Windows 8 PC last night. So far I don't have the 4797 events. But those were and on and off again event. So I will wait longer. But I am still getting the 4624, 4634, and 4672 events.
As for the systems I upgraded to Avast 8, my Windows 8 system with Avast 8 still had the 4797 event. So overall I am still not convinced it's related to Avast.