2004 LS Cannot put transmission in park

Just started a few minutes ago. It actually started after I put the car through a car wash. Don't know if it's related. But immediately after exiting the car wash, I noticed I couldn't put the car in park. It feels like the button on the shifter (it's in the center between the seats and not on the steering wheel) doesn't push in all the way. But I just tried a small test. I can move the shifter from drive to neutral without pushing down the button at all (as expected) and I push in the button and can move it to reverse (as expected) but I cannot move it to park. So, right now, the only way I can start the car is have it in neutral. I'm just parking it by putting it in neutral with the parking brake on.

Any ideas what to look for? I know tonight I'm going to have to disconnect my battery or that will be dead in the morning.

Ok, I made some headway. I took apart the center console and looked at the shifter. I saw that white plastic thing that clicks into each notch in the "blade" looking thing. I tried lifting that up and seeing if I could get into park without the notches being an issue and still couldn't put it in park. I found what makes it shift to park. There's a small lever that if I push it down with my fingernail, I can shift it to park. I see that when I push the button on the shifter, the button seems to push harder than it used to. But I can shift it into reverse by pushing the button. Pushing the button on the shifter seems to lift whatever enough to allow it to get over that metal blade looking thing to let it get into reverse. But pushing the button doesn't let you get into park. So pushing that lever down allows it to clear enough to get into park. I'm attaching a picture of that "lever" so you can all see what I'm talking about. I'm 99% sure now all I need is a new shifter.

Well, I bought another shifter out of a junk yard today for $50. I got the old one out of the car and found I couldn't shift it out of park without pushing on the lever even with it out of the car. The one from the junk yard, I could. I got the "new" one in the car now and I can shift fine.

The only problem I'm having now is that when I put it in park, I can't always turn off the ignition all the way so I can take out the key. I need to push the shifter up a little more and then I can get the key out.

I'll take it apart in a few days again and see if I can figure out what I can adjust to make that work right.