Have you recently connected or disconnected a battery?
Mercury 4 strokes have a small part called a "suppression diode". It is a Y looking piece of wire that connects in line between the ignition switch and the solenoid. If you have a power spike, the diode blows and will not complete the circuit. The motor will do everything you say, turn the key on, everything works except the starter. If you connect the battery backwards, it will blow the diode. You might wanna take a voltmeter and start at the ignition switch and trace the wire to the solenoid and start looking for the problem.
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