Hello Vlad. I am using Win 2K Pro and have a similar issue as you. When I recent installed avast! Internet 5.0 my connection gets severed. The hardware 'appears' to want to work but somehow the ethernet hardware is disabled. Magically, when I uncheck the 'avast! NDIS Filter Driver' section in my nic cards property window - the bits start sending and receiving! I don't suggest you do this because what happens is that avast! Firewall becomes 'uninstalled' or no longer part of the program.
I need to find a more 'surgical' approach. A person in GDR (Germany) told me that his (or her) Win 2K system works fine with avast! Internet 5.0 - so I must be doing something stupid.
By the way - I am using Win XP on my other computer and avast! Internet 5.0 works like a champ - no issues. But then again - my home network is much simpler than yours.
Cheers!
Don