Probably a noob question...

So I'm building a arduino robot. I am using the SN754410 Quad Half H-Bridge to drive the motors, with 3 AA batteries external to the arduino. When I plug in the USB cable and upload the code it runs! But my cable is only 3 feet. I bought a 9V battery adapter and plugged that in instead of the USB and nothing happened, not even slight movement of the motors at start-up. So I built a flashing LED circuit and that works fine with the 9V battery.

Is there something obvious that I'm oblivious to?

Current is likely what you're missing, a PP3 type 9v battery is useless at supplying more than a few mA. It will happily feed the flashing LED because that doesn't pull much current, the heavier current draw of the robot gear will overload the 9v battery. Try reading the voltage of the battery with a meter when you plug the robot in.