One click, no start, codes P0133, P0300 and P1682?

The first two codes have nothing to do with the engine not starting so please create a new question to solve those issues. The P1682 code means there is a problem with the ignition switch circuit. There is a ground for the starter relay that is on the right of the engine connected to the cylinder head that might be loose or off. Here are the starter system wiring diagrams so you can see how the system works. Also try to switch the gear selector to neutral to see if that makes a difference. The first stop in the starter circuit is the BCM so of the ground and power to the relay is good let's do a CAN scan to make sure the BCM is okay. This scan is easy, and the scanners are cheap now, you can get a CAN scanner (Controller Area Network) from Amazon for about $30.00. here is a video to show you how. Also please use a breaker bar in the front of the engine to make sure the engine turns by hand.

https://youtu.be/u-4syLc-ifQ

Here is a scanner link:

https://amzn.to/3o41KcZ

Check out the starter wiring diagrams below. Check out the images (below). Please let us know what you find. We are interested to see what it is.

Yep, these readings look normal, the starter sounds like it is bad, you can check for power at the trigger wire when in the crank position to confirm. This guide will show you how, I have included instructions in the images below to show you how to change the starter on your truck.

https://www.2carpros.com/articles/starter-not-working-repair

Check out the images (below). Please let us know what happens.

Please let us know what happens.