Never used a megaCD, but if there is no power light I can't imagine a dead battery is at fault.
Not sure if it uses an external "power brick" power supply or the unit is simply plugged into the mains, but if there is an external PSU (like a laptop) then make sure that is outputting the correct power. Most Sega stuff of that era ran off "9V/10V, 1.2Amps, negative tip."
Are you using the correct Sega PSU? If not, does your psu match the sega one? Make sure you check the polarity (negative tip).