Problem with charging iphone 5?

I've had the iphone since about August, and had no problems with it. Recently, my phone was almost dead, so I plugged it in, and it recognized that it was charging. When I removed it a few hours later, it was dead. When I'd unplug it and plug it back in, it would show on the screen that something had just been plugged in, but it would never gain power, just stay dead. I took it out of the wall charger and plugged it into the computer and it charged perfectly, I started doing that, and then 2 days later, the same thing happened on the computer, I plugged it in, and it would say it was charging, but it wouldnt gain a any battery, just decrease slowly. I then grabbed a new charger at the mall, and tried it out, it worked perfectly. I plugged it into my old wall charger and it worked, and it also worked on my computer. 2 days later, I plugged it in, went to bed, and when I woke it up it didn't gain any battery, it was about the same as it was when I went to sleep, kept trying, wouldn't gain any battery, even though it still said it was charged (same as before). I tried it on the computer again, and same story, says it's charging, but it's not. I assume there's some kind of problem with my phone, but I live far away from an apple store, and I likely won't get an opportunity to go up there for a while, so I'm just curious if anybody has had this problem before, and if they know about how much it will cost to get it fixed?

Try to restore it