Zone Alarm

I think this is security related enough to go in here...

I've had this computer for about a week now, and naturally the first thing I did was stick on zonealarm. But already it says it has blocked 682 intrusions, 580 high rated. Most of these are coming from the same IP addresses, just with different ports and some are home dsl lines. I'm pretty sure I don't have any trojans as I haven't downloaded anything yet and I'm on a dialup so my IP changes each time I connect. Where could all these attempted intrusions be coming from?