Technical issues with Heroes III.

what could be the problem?
firewall is off, antivirus doesn't block connections.

I recommend turning it off. Is it a local network - computer - computer, or is a router being used? If a router is being used, try turning off the firewall on it. You can also enable the IPX protocol - it usually works in a local network, but don't forget to set the network priority if it hasn't been set.