Won't start fro key. Do you have battery voltage to the keyswitch? The keyswitch gets voltage from the positive post of the starter solenoid, goes through usually red wire with fuse, to the keyswitch. If fuse or fuse holder is bad, you get no voltage to the keyswitch. Murray will have safety switch for seat, and brake or neutral switch, and interlock switch, for the deck engagement. Any of the safety switches will keep the start circuit from functioning. Last the key switch may be bad, it neds to be checked with ohm meter to see if the start function is making contact when key is turned to start.
Here is a basic wiring diagram for five wire keyswitch. If I had your Murray number, we maybe find your exact model.