iPhone 3GS (Model A1303) Stuck In Continuous Boot Loop
My iPhone 3GS is stuck in some sort of boot limbo. It reboots in ~ 5 minute intervals regardless of whether it is plugged into a power source or not. After a boot loop exhausts the battery life, the screen prompts to recharge indicating a terminally low battery. Upon plugging into a power source, the battery charges just enough to re-enter a boot loop.
I should note that I have tried three different and new batteries, each one having the same result as the next. As you can imagine, it has been frustrating receiving each and every new battery from iFixit, installing, then hitting this same dead end.
I've thought of other malfunctions: possibly a worn out logic board? Possibly faulty cables? I'm not certain as I cannot test either for functionality.
Just before having this issue, I was using a new battery from iFixit with really stellar results until one day last month, my Bluetooth randomly and automatically attempted to connect and search for devices (which was perplexing). Simultaneously, the phone froze off-and-on, then rebooted and prompted to reactivate with a cell provider as if it were brand new.
I am able to restore with iTunes by placing the iOS in recovery mode, although upon each restore final reboot, the iOS never loads, and the reboot cycle continues. What I have is a brick and three new iPhone 3GS batteries I cannot use. I'm very close to getting rid of the 3GS but any advice would be appreciated.