Do you have another display with usb-c or a usb-c to hdmi adapter to attach to the SS2 ? Then you can hook up the SS2 to the dispplay and see if the logic board is still working and troubleshoot device drivers and what not. If you get no signal to the new display then you know you'll have to send the SS2 to Microsoft for service or replacement.
You also might want to power down the SS2 (remove the power lead .. wait 20-30 seconds and re-attach power lead. Then try entering the UEFI menu (press power button and volume UP at the same time). If the UEFI menu shows up then there may be some hope it is a software/OS configuration issue.