The system should have more than one USB-C port -- does the same happen with the other one? If not, the port is the issue.  If it does -- and the adapter LED stays on before you plug in the notebook end -- the issue is with the system board.  
 hi when i plug my usb type c connector into the XPS13 the light on the connector goes off. The battery is not charging. if I press the 'on' key the keyboard backlights come on, the display very very faintly shows the Dell logo and the light on the USB connector goes on. About 5 seconds later all lights go off again. The laptop wont boot. Any thoughts? I could buy a new power adapter but doesnt feel like thats the problem. one month out of warranty... thanks
XPS 13 9300 type C charger problem