Will not start after Dorman ignition lock switch was replaced without relearn process?

It sounds like you have a bad connection or the ignitions which is bad. Here is the correct way to install the switch but this can help as well:

SWITCH-KEY-IN IGNITION

DESCRIPTION
The key-in ignition switch is integral to the ignition switch, which is mounted on the left side of the steering column. It closes a path to ground for the Central Timer Module (CTM) when the ignition key is inserted in the ignition key cylinder and the driver door ajar switch is closed (driver door is open). The key-in ignition switch opens the ground path when the key is removed from the ignition key cylinder. The ground path is also opened when the driver door ajar switch is open (driver door is closed).

The key-in ignition switch cannot be repaired and, if faulty or damaged, the entire ignition switch must be replaced.

You can try a hard reboot which is done by removing the negative side of the battery, with the cable loose from the negative side of the battery, hold it to the positive terminal for 1 minute this will discharge the memory capacitors in the BCM and PCM allowing the system to reboot.

This guide can help as well:

https://www.2carpros.com/articles/how-to-reset-a-security-system

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

I will definitely let him know as soon as he gets home, and we'll keep you updated on it. Thank you very much.

I didn't install a switch though. And am I supposed to touch the negative cable to the positive terminal?

Yes, you remove the negative cable from the battery and touch it to the positive battery terminal with the positive still connected. There will be no short because the battery is out of the loop (not connected on the negative side).