Dryer Will Not Start; No Error Codes, All Lights Normally

My Kenmore HE3 Electric Dryer (Model 110-82836100) suddenly stopped working. Everything appears normal but when you press the start button all you hear is a beep and a loud click near the control module. I have checked the thermal fuse and thermistor and both are within tolerance. I have checked the 220 power and the machine is receiving the normal voltage. I have run the machine through the test diagnostics and there are no error codes and all of the LED lights are working as indicated. The door switch tests good as does the moisture sensor. I have not tested the belt switch nor replaced the electronic circuit board. Any suggestions on how I could the circuit board before replacing it? Also, should I test all of the other switches and motor before replacing the circuit board?