Sounds like the control for the plow might be wired to one of the TBC(truck body controls) legs in the interior fuse panel.This would account for the dash and heater being dead and if shorted or wired incorrectly, could cause all sorts of problems with the battery.
Very likely it has blown the main super fuse or a fuseable link in the engine compartment.
A quick test would be to jump the starter ignition switch or solinoid, from the main post (big wire) to the ignition post (small ign wire) with the key on it should crank and start.
If this fails you have a defective ignition solinoid or a defective neutral safty switch.
Just my 2 cents worth.Hobert
