I have a 2000 Nissan Maxima. When I press on the gas all of the dashboard lights come on. I press on brakes all lights go out.

Sounds like a loose connection under the dash that is pulling away due to the acceleration "G" force. The fact you did not mention it did it when breaking sort of confirms it. Turn your lights on and reach under the dash ,,, then see if just contacting a wire harness with your hand causes a flicker. Unfortunitly this sort of problem can have many location ... from the fuse box to under the dash ,~~~~good Luck