XPS 9560 Not booting (failing POST)

My XPS-9560 was working the night before but the next day it won't boot. The keyboard lights come on, the power light comes on but no display. Holding D down while booting successfully tests the display, holding FN during boot does nothing. Hitting F2 does not reach the BIOS. When powering it down the fans come on briefly before it shuts down.

The system is 18 months old, all signs point to a dead motherboard but Dell says they can't do anything. Is this just a paperweight now with nothing to be done?