USB C port almost confirmed to have issues. (Bad news its on motherboard)  I believe same USB C device are working fine on another machine,  You can attempt OS or Driver reinstall, but symptoms almost confirm you have a Bad type C port on the laptop. May be Dell realized this limitation and future XPS 15 and 13 models have more than 1 type port.    Even after replacing Motherboard You will need a regular non Type C charger anyways, cause Monitor will keep supplying power to the C port.  If the monitor is not a very High Resolution one, a USB A to HDMI adapter can be used as well.  
Hi,I have a XPS 13 9360.I'm attempting to connect an external monitor via a USB-C to HDMI adapter, however it isn't working. I get the notification "PC isn't charging" when I plug in a monitor via the adapter.I've tried two different adapters. Both adapters work with another device (my mobile). One of the adaptors previously worked with this laptop when connecting USB-C to VGA, however connecting USB-C to VGA no longer works anymore either.  The adapters I have tried are the Anker USB C to HDMI Adapter and the RDII 6 in 1 Multi USB-C Hub. I have also tried multiple monitors, but none have worked. Does anyone have advice? Thanks!
XPS 13 9360 usb-c to external monitor