Here are your parts
Replacement parts for WHIRLPOOL LET6634DQ0 | AppliancePartsPros.com

Here is the wiring diagram
https://www.servicematters.com/d...0Sheet%20-%203401728.pdf

The above is pretty blurry so he is the wiring from a different model but it looks the same as yours
https://www.servicematters.com/d...0Sheet%20-%203406688.pdf

Does your interior light work as it uses the same side of the line as the motor. Also if you just looked to see if the breaker was OK, turn it off/on a couple times slowly. Sometimes you can loose half the line without tripping the breaker. Best to check it with a meter.

High on the list is the thermal fuse in the motor's circuit. This is item 8 in Section 3 (on the blower case).
If you do not have a meter you can check it by:
Unplug the unit. THIS IS CRITICAL AS A DRYER USES 240 VOLTS WHICH IS LETHAL.
Short the two wires from the fuse together
Tape them up so they cannot short to the frame
Plug it in and give it a try.
If the fuse is blown replace it ASAP as it is a critical safety device.
Also clean and check your vent system and the blower wheel.
Often the cause of this fuse blowing.

Other likely suspects are the door switch and the push to start switch.
Hold the door switch in manually to see if it is just the actuator.

All the above can be checked with a meter with the unit unplugged which is the safest way to do it.

I would suggest you purchase a meter. You can get a decent digital multimeter for under $20.00. You do not need fancy though it is nice if the leads are a couple feet long.
If it saves ordering one unnecessary part it has paid for itself and you end up owning a useful tool.
Most places will not let you return electrical parts so if you order it, you own it.
A couple things to watch when measuring ohms and continuity
1. Always remove power from the machine otherwise you could blow your meter.
2. Always disconnect at least one side of any device you are checking. This eliminates the possibility of measuring an alternate/parallel circuit path.
3. When checking for closed contacts and continuity use the lowest scale (Usually 200 ohms). Then try higher scales. This scale is 0 to 200 ohms so if the device you are measuring is 300 ohms this scale would show an open circuit which it is not, you are just measuring outside the scale's dynamic range.

There is a good STICKY at the start of this forum about it's use.

This should help
http://www.applianceaid.com/wpdryer_how-to.html

Start at the following line as you should not have to take the front off.
To go further in the disassembly, lift the cover from the lint filter or if yours is the one with a filter and cover together, remove the whole filter.