A router should take care of most direct network attacks from the internet which is the main purpose of Zonealarm and the like. Without a router, ZA and others are required for even basic security due to all of the security targets available on Win XP. Protection is best done with a bit of hardware like a router - ZA is a good layer but is known to not shut down in a timely way.
The remapping error is typical when the user's space at logoff is unwilling to release all of the memory space upon logout.
If this is a repeatable issue, perhaps before the offending user logoff, you could try killing suspect processes one by one until the event viewer is happy and reporting nothing - that is if the issue is consistent.
One suggestion - please ask your wayward user to backup things like Outlook Express email folders and accounts - MS Outlook PST files if they use MS Outlook (no express), their favourites, the Desktop and their My Docs and subfolders - just in case Windows uncerominously 'decides' that their hive is no longer 'viable.'
Good Luck!