Ответ на "no signal, motherboard or antenna issue?"It could be an issue with the SIM card not touching the metal plates on the phone resulting in the no signal issue. However it could be the software could be functioning abnormally so restore the phone. But if none of these work then you could try contacting your phone carrier to see if they blocked you from calling.
Ответ на "Can I take the screen out, without turning it off?"Yes you can but there is a risk of you hurting yourself (small electric shock) or a greater risk of the phone being damaged with contact of water since the phone is on. Just make sure that the exposed motherboard does not get into contact with anything so that no extra damage is done