Hi! First I would remove all extraneous devices in order to rule those out -- extended RAM, battery. You've ruled out the charger and DC-in, which is good. Next, although unlikely to the be issue, it's worth wiping the HD and reinstalling the OS. I'd go into Disk Utility and do a check on the drive as well, just to see if it reports that drive failure is imminent.
It appears you have the model iBook with the integrated Airport. You can remove it...it's just more work because it's not a "user serviceable" part. Here's the replacement part:
I've never heard of Airport problems like you describe, but if what I mentioned above doesn't help, it may be worth opening the machine and swapping the Airport card. But before spending the money, I'd simply remove it, and verify that the laptop does not freeze when it is minus an Airport. If it behaves and does not freeze with the Airport removed, that's a pretty good indicator that the Airport is the issue. If it does freeze without the Airport, I think it's pretty safe to say at that point that you've got a logic board issue.
One more idea -- you might try booting off of another machine's hard drive using Target mode. If your machine still freezes while running off another machine's hard drive, that rules out your hard drive as the problem.
Yet another idea -- I wonder if it could be an overheating issue. Do you notice that the fan is on at all? You might want to download a utility that monitors the fan/heat situation (I don't recall the name of one at the moment unfortunately) in order to see if an overheating situation may be locking up the computer.