Here are your parts
Model LER5620KQ1

Here is the tech sheet
https://www.servicematters.com/d...0Sheet%20-%208528187.pdf

Usually a hum is the motor running or the motor trying to run.

If the unit produces heat but the drum does not rotate then could be just the belt is broken.

For a motor not starting.
Rotate the drum by hand, it should rotate fairly easily. If not then you have a mechanical problem.
If it does rotate. With the door open and the door closed switch held closed, push start and rotate the drum in the correct direction. May take two people to accomplish this. Watch your knuckles in case it starts up.
If it does start this is a good indicator that your motor is shot.

No
If you check the wiring diagram the door switch disconnects the Neutral, therefore the motor cannot get power.

The No of coarse assumes the hum is coming from the motor.

It took two of us but we held in the door latch switch and pushed the start button and tried to rotate the drum.
Did the drum rotate fairly easily. It should

You can hear the motor start up and feel heat but the drum wouldn't turn.
That the unit started to heat is an indication that the motor is turning.
There is a centrifugal switch on the motor that turns on power to the heating elements once the motor starts rotating.

The belt is still tightly on the drum. I didn't take it completely apart so I didn't see the motor but if you can see the belt snugly on the drum it should probably be fine right?
Right. Should be but it is not.

Sounds like for some reason the belt is slipping on the motor.
You will have to remove the drum to find the cause.
Pay extra attention to the idler pulley!!

Could be the centrifugal switches are actuated.

When the motor is at rest
Switch 1 connects the motor's start winding into the circuit
Switch 2 removes the heating element from the circuit.

When the motor starts to rotate
Switch 1 removes the motor's start winding from the circuit and the motor runs on the main winding
Switch 2 connects the heating element into the circuit and you get heat

Could be the mechanical assembly in the motor that actuates the switches is broken or jammed up with lint.

The drum will not spin very far if at all after rotating it by hand.
Sounds like it is rotating OK

Cannot tell where the shavings are coming from.
If they are metal something is rubbing where it should not

The motor is $81.86 not including shipping etc. from this site.

Not actually doing the testing myself I cannot tell.

But looking at the tech sheet a black wire goes to the Start/Main centrifugal switch. What it does is provide power to the motor after the start switch is released RE: is in parallel with the start switch.
Holding the start switch closed will test this.
If it runs OK with the switch held closed then it may be the problem.