The dryer kept turning endlessly and it puts out no heat. I replaced the timer and the dryer cycling thermostat and there was no change. It still keeps running and no heat! What could cause that?

Here are your parts
Replacement parts for WHIRLPOOL LEB6200PQ1 | AppliancePartsPros.com

Here is the wiring diagram
http://www.servicematters.com/d...0Sheet%20-%208576793.pdf

Have you turned the 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.
In this unit the heater and timer motor run on 240 volts, so if the timer is not advancing and no heat in Timed Dry mode, odds are high that you have a problem with the 240. The main motor on the other hand runs on half the line (120 volts)

Next I would check the heater, should be approximately 10 ohms.

Then the thermal cutoff (Item 9 in the "Bulkhead parts" section), should be 0 ohms.

If the thermal cutoff is blown be sure to give the interior a good cleaning including the blower wheel. Also clean and check your vent system.
Note that the cutoff comes with a high limit thermostat and both should be replaced.

If you do not own a meter, I would suggest you purchase a one. 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.