Have you tried both strings (separately) and does it seem to stop the pings? If the pings aren't being logged anymore, I wouldn't stress about it. But I'm not sure if it only applies to Win98 and WinMe only or to all O/S...I'm sure a moderator will be along to clarify this.
I only had one problem of my PC rebooting when trying to scan the HHD since I've installed avast (which by the way was build 183(?)), and at first I had thought it was avast acting buggy but it was a hardware problem, which I'd overlooked, but solved eventually. Never locked up on me though.
If you're having problems with avast locking up, my suggestion to you is to start a new post. The moderators will give you all the help you need
¤estatik¤
*edited*Didn't see your post, opps, delete last sentence.