Unfortuantely it sounds like some humidity issue has caused some liquid damage, possibly in your charger port area. Have you ever had the phone in bathroom with you when having a bath?
I had poor battery issues with my phone and the first thing they did when I got to Genius bar was check for water damage (luckily that was all fine). After that, because of the issue with not being able to power off and poor battery they replaced my phone. They wouldn't ask for the money unless there is water damage there. Water damage doesn't necessarily mean you soaked it in water, just a few droplets from somewhere have entered the port. Unfortunately, according to warranty terms and conditions if you want it replacing you will probably have to pay them.