It could also be a short in the control wire to the thermostat, or possibly a failure of the furnace control board. If disconnecting the thermostat wire as suggested by Todd doesn't help, I'd try disconnecting the control wire at the furnace end (which may well not be very easy to get at) and seeing what happens. If the furnace doesn't run, it's clearly the wire; if it does, it's some problem with the furnace itself.
If the thermostat (or furnace) is in a slide, one possible point of failure for the wire is the segment that moves when the slide is moved.