L293D motor shield power sources

You need separate power supplies. Use a 4xAA for the motors and a 9V for the Arduino.
There is a jumper next to the motor power in plug which is labeled "PWR." (the little yellow thing)
That jumper connects the motor power to the Arduino power.

Pull it off and plug it back in on only one pin so you don't lose it.

You may want a heftier motor driver. The L293 cannot pass much power because it uses bipolar transistors internally which have a very high voltage drop.