Hello, I have the same problem with my Sony L, when I plug different usb cables and/or chargers I don't get any sight of the device charging, now I've got the greenish light to light when I plug it in, but it doesn't stop if I unplug the cable and remove the battery. The solution that I came up with was to plug the usb cable in and put the phone and the cable in some kind of box that will put pressure on the cable so that I can be sure it's all the way in and I can position the cable in the right way. I found out that even if i have the greenish light on after a time it will turn to red and the changing process will start. After I get the phone out and start it up and then I put it back, find the best position for the cable (when the charging simbol on the phone and the led light up) and let it charge.
So in my opinion the problem is with the connection between the usb socket and the motherboard, you'll have to go to a specialist to resolver the connections or change the usb socket. If i could load an photo of how I've done it I would buth I can't, so I hope all of you understood what I ment and this helped you.