iPhone 4 won't turn on or even charge!

My iPhone 4 running iOS 6 was not displaying it's charge correctly. I tried to sort it out like I normally would by charging the battery all the way up and then drain it and charge it up again. I tried to do this because, like it says above, it won't switch on. To boot it I tried to hold the power button down then plug it into charge through USB and the low battery symbol was displayed. Then however the iPhone booted up and showed 65% battery. Because it did not actually have enough charge it shut down straight away again. So now I cannot do anything with it. Before you post anything like putting it into DFU mode and restoring it I am not restoring it because I have no backup of the data that is on it. I have also tried holding down the sleep and home button for up to a minute but still no results. Please help!