Not your average "phone won't charge" question, wait for it

Hello,

I changed the screen and battery of my iphone 5c and everything was great until I tried to charge it. The phone said it was charging but the power percentage slowly dwindled down (much more slowly than when it isn't plugged into a charger which makes me think it's getting some charge). So I took the battery out to see if anything looked grossly abnormal (couldn't see anything) and put the battery back in. Then I tried charging it again and it charged beautifully back up to 100%. And when it went down to 80% I tried charging it, and it started charging back up! But then when I waited until the charge was at like 20% and tried to charge it, I start having the original problem again. Like what?? So every time I want to charge my phone and the charge is below 20% or so, I have to take the battery out and put it back in.