The lid switch on your model is located by the left lid hinge under the cabinet. It is activated by a rod on the left lid hinge. If you open and close the lid, you should hear a clicking sound as the switch is activated. If you can't hear the switch, sometimes bending the rod on the lid hinge will correct most contact problems. I haven't seen many of these type lid switches go bad. Its almost always been a simple adjustment to correct a contact issue.
Now, if you are sure you switch is good, the loud hum sounds like you have a drive motor seized up. Try removing the motor to see if it will free spin. The following link explains how:
http://www.fixya.com/support/r599953-replacing_drive_motor_kenmore_or
The motor comes out fairly easily if you follow the steps in the link provided. This will make the motor more accessible to you. If the motor will free spin, check the motor windings by taking resistance checks to be sure. There should be a wiring diagram located inside the operator console.
Your motor also has a motor start switch. If the motor and windings check good, you may have a defective start switch. I apologize for not having definite solutions here, but I'm trying to be as thorough as possible. Its often hard to determine a cause based on some symptoms, as there could be several possiblities.
If you go to searspartsdirect.com and type in your model number, there's an excellent exploded view diagram of the drive components under the "Brake/Clutch/Gearcase/Motor and Pump" heading. The drive motor and switch are listed as items 19 and 20. The lid switch is located under the "Top and Cabinet Parts" heading as item number 11.
I hope some of this information is helpful to you. Let me know if I can be of further assistance to you.
thank you for the information will investigate
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