You will find that most of that is just normal internet *noise* and also your ISP checking to see if you are online etc. Not necessarily targetting your PC, though a % perhaps is.
Zone Alarm is just doing it's job .

Zonealarm is pretty good. In affect, as we so speak now... many intrusions ATTEMPTS has been made already...

And don't bother to know the attempts.. unless ya running a multi million tech business.. and everyone's targetting you...

I believe Zonealarm is accurate... but perhaps.. sometimes.. a little oversensitive..

but it dosent hurt a bit rite?