Are you connecting usung a USB modem ... wireless ... or a router?
usb or wireless will both eat a fair chunk of processor
Possibly that's because zone alarm is a firewall!!!!
It's just coasting when you're offline
even if it's ZA Isec ... unless you are doing something ... it's only listening.
as soon as you hit the net ... it's like a dog ... bouncing, sniffing everything that passes it ......
What's your network traffic telling you?
if you leave the machine ... and it's still sending data ... you got a gremlin.
whiffey is right ... you need to look at what's running ... if you come back ... you need to include everything in task manager's processes list.