Q: not starting low AMP

I plugged my IPOD charger/FM transmitter into the cigarette lighter for about 10 minutes while the car was turned off. I came back out and the car woudn't start. The battery, alternator, starter all tested OK at the repair shop. I used the IPOD charger again yesterday and unplugged it before turning the car off. I came back out again 10 to 15 minutes later and the car woudn't start. I took it to another repair shop and the tests came out OK except the "Starter AMP draw was low with OK starter voltage." It also said to "check starter curcuit for loose warn or corroded wiring." My cigarette lighter is short-tempered. 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 wiring system? Is this a possible cause for my problems?