How do I get my phone to power up when nothing is responding?

My phone was working perfectly fine. After using I put the phone down, and out of the blue the phone went to a reboot power up. It was stuck on the white Motorola screen for a while. I. Turned the phone off and then tried turning it back on. It did the same thing, and went to the white Motorola boot up screen. I was able to power down a few times and tried turning back on only to have it get more difficult each time just to get it to power up. I tried leaving it unplugged overnight and plugged it back in, in the morning. I got my home screen, a green light, and it showed that it was charging. It was plugged in with the turbo charger for about an hour but got no higher than 4%. I powered the phone off and had a real hard time getting it to power back on. I tried holding the power button along with the volume buttons and it finally kicked back on while going to a Droid menu screen but nothing worked not the buttons nor the touch screen. I was able to do this about 2 times. And since the last power down I haven't been able to get it to come back on.

I have since then gotten a replacement phone. Same phone. I tried removing the motherboard and switching them, and still no response. How can I fix this? How can I find out if it's my motherboard that is no longer working? How do I find out if maybe there's a bad connection somewhere on the motherboard?

Please if anyone else has had this problem and can help I'd greatly appreciate it.