As far as motherboard breaking this is the best case scenario. You have separation of the regular WiFi module and the cellular module. This thing is soldered on with a flex connector---so that should be a straightforward fix.
It would seem like the iPad wouldn't care whether or not the 4G piece was attached, but in my experience I've had an iPad freak out like that when I put a CDMA board into a GSM housing for example. I would set the board right first, and then troubleshoot the reboot problem.
jessa