Oh yes, I've seen a similar problem a few times. As far as I remember, Google reveals quite many hits for this problem, without any relevance to avast!.
It seems (but this is really just a wild guess) that installing avast! somehow changes the order of some initializations performed during the Windows boot (for example, OLE might be initialized earlier with avast! that without) - which results in described problems, probably due to some glitches in Windows 95 itself.
I'm afraid I don't have any solution... some of the Google results suggested that upgrading Internet Explorer to a newer version might help. I think it's worth trying (if you have a very old version of IE right now), but I can't guarantee it will helpĀ