iPhone Chargers

About a month ago, I bought my sister and I an iPhone 4 (previously owned). Both of us have been having trouble with charging our iPhones. Hers was the first to start having problems and mine started today. We've tried different cords and boxes - sometimes it will work and sometimes it won't. When it didn't work we tried turning them on and off and that worked occasionally. I don't think there's anything wrong with the battery but I'm not positive. Any advice would be helpful, thanks! (Not sure if this is in the right category as I've never used Apple Support Communities before.)