If the battery ran out, it sounds like something was corrupted when the power quit. Shut the phone off. Remove the batter, sim and sd card and then replace everything and turn the phone on. If that doesn't fix it, you may have to perform a factory reset.
If you had a decent charge and the phone just went black in the middle of the call, you could have had a memory failure in which case you'll need to get it serviced. Is it still under warranty?