Phone shuts off and has trouble rebooting

My phone is randomly shutting off and then going into "reboot loop" while off the charger. If it manages to reboot on it's own, then it will not be able to find my location. It will stay on for about 3-5 minutes before shutting back off and entering the reboot loop.

I know my battery is swollen from a prior overheating, but it has been that way for months with no ill effects. Also, every time I turn my phone off and then back on, it will say it turned off due to overheating. Could these problems finally be catching up with me? Or is something new going on. I don't want to throw parts at it to see what works.

I know I need a new battery, but is the motherboard also toast? Thanks for the advice.