IPhone only charges when completely off?

I have an iPhone 5c and just tonight I realized it will not charge unless the phone is completely off. I've tried a reset and if made no difference. What causes this and how can I fix it?

This is very odd. You must only use Apple certified chargers, if you are using third party chargers you must stop as there have been many reports of issues like these with 3rd parties. Other than that I would strongly advise you to give Apple a call (visit their website for more details on contacts) or take it to your local Apple Store or Carrier Store - or a store you purchased it and explain to them - perhaps it's a manufacture problem and they'd replace it for you.