are you behind a router??
if so then there is probably a problem, or another machine on your network is also infected....however zone alarm shouldn't block connections like that, my guess is that you are connected straight to your modem, straight to your ISP...in which case, you will probably get a lot of intrusion attempts
for the most part, it's script kiddies who download port scanners and try to log into any machine they can. If your zone alarm is catching that, then there's nothing to worry about, but just make sure to keep your windows updated and your zone alarm updated