Some plot holes?

I always wondered why Dooley didn't keep the engines running after he landed? He would have had radio power to possibly get his location known before he completely ran out of gas. I'm sure an experienced pilot like himself would know that engines in -70 weather would be hard if not impossible to start.

Also, when the radio man knows he's running out of battery power, why wouldn't he tap out to his rescuers to just tune in on the 'coffee grinder" and locate them by the radio compass in their planes. That's how they found them in the end.