My son's Inspiron 7347 stopped charging too, and additionally it wouldn't function when plugged in to the adapter without the battery. He found that he could get it to charge if he compressed it with a stack of books. However, over time even that stopped working. I ended up removing the motherboard and I discovered that the solder joints on a diode had broken, and the diode had shifted so that it was no longer making contact with the pads on the board.The problem was that the board standoffs were of insufficient height to prevent the components of the top motherboard from touching the polymer separator between it and the bottom motherboard, and rough use caused this particular solder joint to fatigue and break. After the most difficult soldering job in my whole life with the tools I had a hand at home, I managed to locate the diode in the correct position and reflow the solder enough to get it to bond. Having it come to life again was about the happiest moment in recent memory. Not a task for someone without the correct tools
and fine motor skills.