Re: Cortex not working, no robot light lilluminated
This is a link to what the LED codes mean on the Joystick and Robot: http://content.vexrobotics.com/docs/Cortex_Joystick_LED_Codes_052010.pdf
You should be able to use it to diagnose exactly what the problem is.
It still sounds like you have a low battery. Is it possible that the battery you swapped it with was also low?
I would recommend starting over the Setup process, and following every step - Downloading Master Firmware, ROBOTC Firmware, syncing with the joysticks, and seeing if that resolves the problem.