Truck starts by itself

My truck turns over and attempts to start although the key is off, Starter and starter switch has been replaced. Cannot find any wires shorting out, any ideas?

     LOW VOLTAGE. I HAD THE SAME PROBLEM WITH A RIG. CHANGED THE STARTER TWICE. THEN I HAD THE BATTERY CHECKED OUT, AND EVEN THOUGH IT WAS ONLY A YEAR OLD, IT WAS NO GOOD. ALSO CHECK THE BATTERY CABLE TO THE STARTER. IVE SEEN THESE SHORT OUT AGAINST THE EXHAUST MANIFOLD AND CAUSE THIS SAME PROBLEM. IF NOT FIXED THEY WILL CATCH FIRE AND BURN YOUR RIG TO THE GROUND. GOOD LUCK