why does my iphone only charge when its turned off?

why does my iphone only charge when its turned off? and it isnt does seem to show on my laptop!! well it all started 3-4days ago i brought a new laptop and i was backing my iphone up to my laptop but the net kept lagging so i thought i'll try it the next morning, i left it on charge then turned it off as soon as it hit 100, i woke up in the morning and saw my usb cable ripped thats when i realised my phone wouldnt charge!! HELP!!!