[old Chevy guy]

check all your battery connections and your ground to the block and the body and your plus side to the starter. then check your connection to the solenoid from the purple wire. sound like the battery connections are bad or the solenoid is junk or your battery. have you had the battery load tested? even if the starter was bad the solenoid should click if the battery is charged . even if there was a draw it should crank with a charged battery and even with a draw I doubt anything but a dead short would kill the battery in 5 or 10 minutes. curious to see how this one plays out.