2004 Saturn L300 Starting/Battery Problems?

I left my iPOD charger/FM transmitter plugged into the cig lighter for about 10min while the car was turned off, came back out and the car wouldnt start. Took it to the mechanic, battery, alternator and started tested OK. Used the iPOD charger again yesterday, unplugged it b-4 turning the car off, came back out 10-15 min later, would not start. Took it to Advanced Auto Parts for testing, all results OK but it said that the "Starter AMP draw is low w/ OK starter voltage. Check starter circuit for loose worn or corroded wiring". My cig lighter is "testy" and if you bump whatever is plugged into it, it comes unplugged a little and shuts off whatever is charging, could this cause a short in the electrical to cause these problems???