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The mid section gets hot because the compressor is overheating and that is usually due to the fan not running which you have already confirmed. Now you just need to test power to the fan motor to see if it's getting power or not. If it's not getting power, then replace the control board which sends power to the fan motor. If it is getting power but the fan isn't running, replace the fan motor.
If you don't have a multimeter to test power/voltage, then feel the fan motor. If the fan motor is hot then it's getting power for certain so replace the fan motor. If it's not hot, then likely the control board needs to be replaced.
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