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Replacement parts for WHIRLPOOL LE5800XMW1 | AppliancePartsPros.com

I cannot find a wiring diagram for this specific unit so the following involves a bit of guessing.
Looking at the parts, this unit has:
1. A control (cycling) thermostat mounted on the blower wheel. Not sure why they list it is as Items 2, 6 or 7 in Section 3.
2. A thermal fuse (Item 8 in Section 3) mounted on the blower wheel
3. A high limit thermostat (Item 15 in Section 3) mounted close to the heating coil.

First try flipping your breaker off/on slowly a couple times. Sometimes you can loose half the line without actually tripping the breaker. Better yet check it with a meter.
L1 to L2 should be 240 volts.
L1 to Neutral and L2 to Neutral, both should be 120 volts.

The most common cause is a blown thermal fuse.
Unplug the unit and check the fuse with a meter should be 0 ohms.

Jiggery Pokery method is.
Unplug the unit.
Remove both wires from the fuse, short them together and tape them up so they will not short to the frame.
Plug the unit in and give it a try.

If blown, replace the fuse ASAP as it is a critical safety device re: prevents lint fires which can turn into house fires.

Also clean/check your vent system and the blower as these are the most common causes of it blowing.

If the fuse is OK then I would check the door switch and the push to start switch.