open zone alarm and go into the tab "program control"
find mirc.exe (if it is not there add it, using the add button down the bottom right of screen)
make sure that mirc has 4 green ticks.
If this doesn't solve the problem you may need to tell zone alarm to allow certain ports through..
You should allow:
TCP Port: 113 (for Mirc Ident)
TCP Ports: 6660-6669 (for chat)
TCP Ports: 1025-5000 (for dcc, if you want this feature)
cheers