Will not crank

I drove it for a few days after buying it from an aircraft (jumbo jet) mechanic who works on his own vehicles as well (Audi's and VW's). He said that he ran a computer diagnostic before selling it to me. There where no problems but a sensor in the exhaust system that may replacement. The last day I turned the car off the headlights stayed on, and drained the battery. When starting it the next morning it cranked twice, then nothing, all lights and radio working. I tried briefly jumping it an no crank, I charged the battery at Autozone. Still not cranking. Meanwhile when I turn the key the radio lights up, and the headlight remain on without the key in the ignition and will not turn off with the headlight switch. What is the most probable issue with my car? I am not going to spend more money I do not have repairing anything that costs more than I paid for it.