Equinox 2005 Ignition?

About four days ago I went to start my car, I had the cab light on because it was night. I started my car and turned off the cab light, my car instantly shut off and would not start back up or the dash lights will not turn on. I hooked up a battery charger and set it to jump start but nothing. When I put the key in the on position and move the shifter up and down the dash lights will flicker as if the battery is low but the battery is fully charged with 12v reading. I even checked all fuses, under the hood and in the cab, and all fuses are still good. Whenever it feels like it, it will start and runs normal and fine. Could it be the ignition? Or is it an electrical problem? I have an after market radio installed and even switched it back to the stock radio to be sure it was not my radio draining the battery or causing a short.