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Parts for Whirlpool GEQ8858JQ1 Dryer - AppliancePartsPros.com
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See the attachment for the tech sheet
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Is there a way to bypass the circuit board to test if that is bad?[/COLOR]
This will not do you any good as it is not part of the start/motor circuit. It just controls the timer motor.

First I would check the power. Other wise you could pull the unit apart only to find the problem is not in the unit.

Try flipping the breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker.
Check the voltage at the wall receptacle
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
Do this with the heater off and on.
[COLOR="Red"]Be careful as 240 volts is lethal !!![/COLOR]

If the power is OK.
Unplug the unit and set the timer to mid cycle timed dry.
Use you most sensitive resistance meter scale. Also before starting short the meter leads together so you know if there is a zero offset in the meter.

Attach one meter lead to the L1 prong on the line cord and leave it there. Now work your way through the start/motor circuit.

BK and BU on the timer should be 0 ohms.
Push the push to start relay. Both sides of it's contacts should be 0 ohms. I think the blue wires.
All further tests are with the push to start activated.
Both sides of the thermal fuse on the blower should be 0 ohms.
Both sides of the belt switch should be 0 ohms. I am assuming that the switch is closed.
4M on the motor should be 0 ohms.
5M on the motor should be about 1 ohm (motor windings).
Timer switch 4 (W to T) should be about 1 ohm.
Blue on the door switch should be about 1 ohm.
Activate the door switch. Now the other side should also ne about 1 ohm.
Neutral (white) on the terminal strip and the neutral prong on the line cord shoul also be about 1 ohm.

You should have found the open somewhere during the4 above, I hope.