iPhone turns off by itself and requires a hard reboot

I have an iPhone 5c I bought from someone to fix. The problem is no matter what percentage I charge the battery up to when I unplug it after about 2-3 minutes the phone will turn itself off. The only ways to turn it back on is to either do a hard reset by holding the power and home button for 15 seconds or disconnecting the battery connector from the logic board and reconnecting it, which then the device powers up just from holding the power button. I have tried using 3 different NEW batteries but the same thing happens. The connector looks fine from what I can gather. Any and all thoughts help, thanks!