My macbook pro won't charge unless it's powered off

It started about 8 months ago when I was playing a game. The battery was about to die so I plugged it in. The light didn't show up and I got worried. So I shut it off. I tried charging it when it was off and it was fine. I've been doing this since the problem started. Sometimes it does charge when it's on but that has only happened in 2 occasions since the problem started 8 months ago. It really started to become a problem today when I was playing League of Legends and the battery was about to die. Fortunately the game ended in time for me to shut off the computer. I hate having to shut off the computer in order for it to charge as I can't play for longer than an hour and a half before I have to get off. Anybody have any tips.

My Magsafe is clean and free of debris both on the computer and on the plug. I also just tried resetting the power saver setting to default (I had them to never for quite a while (I download very big games from Steam and when the computer is sleeping the game doesn't download)) It worked, for a couple of seconds. I'll keep the default settings and try again tomorrow.