Computer shuts down when I get online...HELP!

When you say you re-installed OS X did you actually do an archive and install or an erase and install? If you did anything different from those choices that won't give you a clean system folder.

Also you should pop in your install disk and go to the install screen and choose "Utilities" in the menu bar then "Disk Utility"
and choose "Repair Disk". It will repair any errors on your drive and let you know if there are any errors. Sometimes you will get errors due to certain installed software or modifications of the OS.

 

What does it say in the panic.log? Can you post it? It sounds like a kp due to the Airport, so you might want to try to go online via ethernet and see if it makes a difference. If it does, it sounds like a faulty Airport card. It might just be loose, so you can try open you iBook up and fastening the card.