IPhone 4S doesn't hold charge?

My iPhone 4S has stopped taking in charge, but when plugged in, the percentage never increases. When it reaches 0 percent, it turns off, and only turns on when plugged in. When unplugged, the phone shuts off. I replaced the battery, but the problem still persists. I tried testing the logic board in different iPhones. But the problem happens on each iPhone, so it can't be the flex connector from the docking port to the docking flex connector. When plugged in, it acts as if it is charging. It makes the sound, has the charging indicator next to the battery, but the percentage never increases. I somewhat know how to solder and unsolder, but I never tried to do it on something that is very delicate, and have to be precise. I looked everywhere on the internet, but no one had the same problem as me. Please list the possible causes, and a probable solution to the cause. Thanks.

Note: it is running on iOS 7.0.4, unjailbroken. I'm not updating, no matter what.

Another note: This is a logic board I bought off eBay, and thought I could fix it. (I have very good experience in fixing damaged iPhones, this has be dumbfounded)

Added (1). Carrier is Verizon, and replacing the charge port requires very delicate soldering, and I don't have the skills.

So you did replace the charge port? I only say this because one time I had a customer who would charge his phone in the car. Problem was that over the winter the salt damaged his charge port. Even though it would show charging it just never would charge. We replaced it and it worked right away. What is the carrier for your phone?
-Ross

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