I bet a sat phone like that would turn itself off if no communication was found, to conserve batteries. And of course we all know there will be no communicating with satellites, right?
Here is the odd thing. Coming to the island wrecked a 747, we saw that. It took apart a chopper, we heard that, but Desmonds boat was good enough for one guy to fix again.
AND, i guess that's what happens to people who aren't sedated or strapped in, the parachutist looked pretty worse for the wear on the last 'leg of that journey'... Ethan was right