First you should check whether the date and time have reset after disconnecting the battery. Go to Settings -> General -> Date & Time to deactivate the automatic time setting. Set your timezone, reboot your phone and you should be good to go.
If you still can't get a connection try the following: Check the little antenna cable right above the speaker module. It needs to be connected to the logic board.
Also, make sure the small blue chip next to the antenna connector is not damaged. It is essential for cellular signal reception.
Another source for connection problems is this connector:
Check to see if it’s properly plugged into the logic board.