My bet would be on your batteries. Insufficient voltage will do odd things to your truck, and you wife's car's charging system is completely inadequate to supply the amount of power a diesel truck needs.
My suggestion would be to throw the jumper cables on the truck and leave it for AT LEAST 15 or 20 min to put a proper charge into the batteries, disconnect them and then try again so you're not bogging down the car and trying to pull 1000 amps through your poor jumper cables. I've had the block heater thing happen to me too, moisture in the GFI plug for the block heater froze and popped the plug, came out in -18 to my truck solid cold... oops. LR
'09 Ford Ranger FX4 with a mean owner