Run diagnostics to confirm the system integrity. It may be possible that the shorted cable damaged the adapter. If all else fails you could purchase a USB Ethernet adapter such as available at Amazon here.
My Precision T3500 connects to internet with Ethernet cable.  It was working fine for years, then a rat chewed up the cable. I have tried two new different cables, restarted everything following the Dell troubleshooter. Still get "ethernet cable not connected" error.  Router is Comcast business.   
Precision T3500 no internet after rat chewed cable. New cables don't work.