I went to dry a load of clothes and when I pushed the start button nothing happened.
I noticed that the timer was ticking and was doing so even in the off position, then I noticed the dryer was still getting hot, so I kicked the breaker off to avoid a fire.
When I looked behind the dryer, I noticed that the vent pipe had gotten crushed over time (my fault).
So, I'm guessing the thermal fuse went due to the high heat, resulting in the non-start, but I'm not sure what would cause the dryer to continue to heat even in the off position.
I do have a multi meter, but I wasn't sure what to test or in what order.

halfmoon--- you also may have another problem that your heating element is shorting out against the heater can. The heat should not be on unless the motor is turning the drum and fan. There is a centrifugal switch that closes a set of contacts completing the 240v heating circuit. So if this is true It may also be the cause of the thermal fuse blowing out.
Unplug your machine remove the back cover. Watch Matt in the video associated with this link how to access the heating element.
Whirlpool 279838 Whirlpool Dryer Heating Element - AppliancePartsPros.com
He is showing how to replace (which I suspect you will have to do) but when you gain access then take your multi meter and test for continuity from one of the heating element connections and the heating can (case). Then do the same for the other connection. If you have a dead short (continuity form either lead and the metal case) then you need to replace your element. That video is associated with the part you may need.
Also check for continuity across the thermal fuse as thorning suggested.
Here is a link for that part and a video of its location.
Whirlpool WP3392519 Dryer Thermal Fuse - AppliancePartsPros.com