Got iPhone 4S wet, then got new battery, now shuts off when unplugged?

Okay, so I got my iPhone 4S wet (got in the pool with it in my shorts' pocket, lol.). We dried it out in rice and took it apart and dried it, but my phone would only stay on for like 15 minutes at a time. It would turn off, then reboot and turn back on.
So, we got a new battery, and it worked fine until I unplugged it. As soon as I unplug it from charging, it turns off!
What could be going on?
I Really don't have 200.00 to spend on a new phone!

The charging port might be messed up if its not taking charge