Thanks, everyone! It worked! Almost immediately after I posted, I got a text that they got it started and would be on the way shortly.
x-post from Beep Me!: Four hours--and a whole lotta ~ma later--it magically started. They were so eager to get home they had the throttle at 102% flying at 548 knots. They made it from Elizabeth City, NC to Georgetown, DE in 14 minutes. Now to tear the jet apart to figure out what the hell is going on...but not tonight. They just want to drive home and get some sleep.
brenda, amych whittled it down perfectly. "Airplane sad!" is about the easiest way to put it. The onboard auxiliary power unit (APU) is needed to start up the engine so the plane can go "Woosh!" If the APU goes on the fritz, there is no starting anything, and you're flying only in your dreams. The fixed base operator (FBO) at each airport can provide you--in addition to fuel--important things like mechanics and parts to keep the plane in working order. By the time they got to NC to refuel, the mechanics had gone home for the day, so if they couldn't fix it they were shit outta luck until morning. Luckily, it finally started. He should be home in the next hour or so, only 6 hours later than he said. It's a good thing we had no plans tonight!
Calli, I keep meaning to say "Go you!" on the student piloting. If you ever have a yen to go north, fly up to KFDK. The airport is 10 minutes from our house and it's no trouble to pick you up for a day of fun.