IPhone won't turn on

Please help! Plugged my Iphone 5 in to charge last night and when I got up it was not charged. The screen keeps flipping between the battery icon(which is empty except for thin red line) and Apple icon.I am using the original charger and also tried switching to two other chargers. I also tried holding down the on/off and home button at same time but it will not reboot. Just keeps flashing between the two screens I mentioned!