When you say a 6 volt battery - how many cells do you have?

Most controllers run on a minimum of 6 cells - they will have a max rating as well. I suspect that your low voltage cutoff is not allowing any power to go to the motor (a feature used to still give you control i.e. servos work, but no motor control as your battery output is too low).

Try a fully charged 6-8 cell pack and see if it does the same thing. Also make sure your throttle is at idle when you power on both the TX and ESC.

Mike