Battery not charging even though phone recognises charger
I have a C6003 running 4.4 Stock with an unlocked BL and am rooted. The phone screen is cracked at the top third (not smashed, just 2 long cracks) and that third of the screen does not receive touch input, but still displays. Anyway, the phone is currently out of battery, when I try to power it on, I get either a flash of the Sony logo then 3 blinks of the red LED or just straight to the LED, which is normal. I plug it in to charge (tried several USB cable / wall plug combos, up to 2.1A etc.) and the red LED glows solid as it should. Even hours later it still will not power on and gives me the blinking LEDs...It was charging for a total of at least 7 hours and is still not turning on. I have had several battery issues recently but this is the most serious. I am sending my phone in for repair under insurance for the screen but need to back it up first! Any help is appreciated.
EDIT: Quick edit to add the fact that this same issue occurred yesterday as well but it eventually powered on with 15% battery, I used it and it would not charge and so that is why it is run down again. Even when powered on it would not charge, the LED did light and it charged for 5 seconds each time the cable was inserted, but after the 5 the LED would stop and it would stop charging. The phone knew the cable was there though as when it was inserted Stamina mode was disabled (as it should) even though it was not charging?