Replace your battery. It should be able to start the vehicle with the fan running.
I find it weird, too, that some Escorts have the fan that stays running after the key is off, and others shut the fan off and keep it off when the key is off.
I've had a 85, 86, 87, and 88 escort. The '85 and '88 escorts had fans that came (and stayed) on with the key off. The '86 and '87 did not. (Never boiled over either...)
The only thing with the 2 that had the fans that stayed on with the key off is that they had autommatic transmissions, where the ones with "fan always off" when the key is off was a stick-shift.
I have heard of Escorts with standard shift transmissions and fans that stay on with the key off.
Hell, I don't know. I just know it's normal on some cars.
Replace that battery.