Disconnect battery. Pull the small wire from the starter solenoid. reconnect battery. If the starter then runs again after you hook up battery, then the starter solenoid is stuck or shorted closed.
If it does not, and if you have a Mercury starter circuit, there will be another smaller relay mounted somewhere near the round connector. Disconnect the battery. Remove the small wire from the small auxilliary relay. Reconnect battery. If starter engages, then this relay is shorted closed / stuck.
If it does not engage with the small wire disconnected, then your starter switch must be shorted closed / stuck.