Why is car starting with key in off position, when battery is connected on 2001 Oldsmobile Aurora

car stopped, just died, try jumping battery and everthing came on but went off, it did that a few times, got a new battety and connected it and car tries to start without the key turned on or in the ignition. Please help me on this!!

3 answers
Replace starter. Solenoid is shorted.
Solenoid fried to start position. Starter is always engaged at this point, need to replace starter.
short in starting system poss repl the whole starter with new solenoid