A couple days ago, I left my phone charging overnight, like every other night. The next morning, it will be 100%, however, when I woke up that morning, it was only 52%, and it just would not go any higher. I was using my original charger and usb 3.0 cable.
After many trials and error, I finally found that my original charger, and my HTC One's usb 2.0 cable will charge my Note 3 at a decent pace.A 5v iPhone charger with a usb 2.0, or 3.0 will still charge very slow.
I assume that my original samsung usb 3.0 cable was causing the problem, but it charges my friend's T-Mobile Note 3 perfectly at a decnet pace. It seems like my cable's problem at first, but the fact that it works on another Note 3, proves it otherwise. Can it be my port's problem not making the connection to the cable, or the battery? The fact that it also charges kind of proves the battery is not involved.
I'm just wondering if anyone is having a similiar problem, and/or can help me fix this before I bring it back to ATT. Quite annoying since I have to unroot.
I've seen the port/connector fail on the S4 - when it does it behaves like you describe. So I expect one or more pins on your Note3 have failed in some way - USB3 uses additional pins vs USB2, so you got "lucky" in that you can still charge via USB2... but the only fix would be a hardware one (ie, a warranty exchange.)
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Today in the car, I was running low on battery, and I only had a 3.0 cable, and decided to give it a try, and it amazingly, it charged. Im assuming that it works arbitrarily. I think some of the pins are loose or defective as you said. I'm going to see if I can use a toothpick to push the pins back up a little. If it still doesn't avail, I'll take it back for an "refurbrished phone"