Binabik: a firewall is a useful thing... .
turning the windows-firewall off means you do not have the control over the progs using the inernet - including possible "bad" ones.
its a good idea for sure to install another one, but step by step.
first you should solve your virus-scanner-problem.
as soon as you got one working fine on your computer, you may try to install a firewall, too.
if zoneAlarm didnt work well, try for example keryo... .