Key relearn doesn't work.

Did you do the three 10 min cycles?Did the security light change state each time before cycling the key for the next cycle?Also why did you take the switch apart?

I did the three cycles and the security light did not go off. The first time I did it, I didn't pay attention to the light so I only did 10 minutes each time. The second time I did it, I noticed the light didn't go off after 10 minutes, so I waited 15 and the light still didn't go off.
I took it apart to check for corrosion or any other issues with the connections because I've had a few issues with the vehicle not starting because of the passlock.

So the car has been not starting off and on then now it decides to not start at all so you tried to relearn the pass lock that didnt work so you took the switch apart and that didnt work ethier?If so you will have to get the body control module scanned which wont be easy since the car doesnt run.The auto parts stores cant do that for free there scanners are advanced enough.Wish i could give you better news.

The car has randomly not started because of the passlock sensor. It was running fine when I took the ignition out. When I put the ignition back in, it wouldn't start so I went through the relearning process.

Sounds like you need atleast a new ignition switch to get back to way it was before.It may or may not fix all your problems.If it started before thats the only things that makes sense.

Well, I replaced the ignition switch and cylinder and that issue is fixed. Now it acts like the key is always in the ignition even when it isn't. When I shut the car off and open the door, the door dings and when I push the lock button it will lock all of the doors except the drivers door. I've check all the fuses and they are good.