Why can't phone detect charger when turned on after replacing battery?

So, let me explain what had happened:

One day, one of my charger ports had caught on fire. It must have been on fire for a while since black smoke was coming out of it. The fire was handled swiftly after detection. My Motorola Photon was connected to the charger when this happened. I found that after that incident, the phone wouldn’t turn on, and I immediately bought a new battery for it. I replaced it and set it to charge via hooking it up to my laptop.

The issue is when I’m trying to charge it. It will charge for a little while (green light), then the phone will turn on (the screen will be on the home screen) for a little while (about 25 seconds on the home screen) before automatically turning back off due to low battery. When the phone is on, it doesn’t show the notification that it is charging. When it’s off, however, it will charge for a little while (about, like, 1 and a half minutes) before turning on. And the entire cycle repeats itself.

Is it the phone that is shot, the new battery is faulty, or should I look into buying additional items to keep it alive? I rather not give up the phone if I can help it still.