While engine is running transmission will not shift into gear

Hello,

Just to clarify, the shift lever is stuck in park?
This could be an issue with the shift interlock. It is what allows you to shift out of park after the depress the brake pedal.
The shift interlock actuator is located under the shift lever (see diagram).
Sometimes the connectors can come loose of the actuator and can cause issues as well as it can be a faulty actuator as well.

Do you hear any clicking noise when you apply the brake to shift out of park?

https://www.youtube.com/c/2carpros/featured

Please let me know little bit more details.
Thank you.

Got it. So when you put in drive it does not engage right?
Can you feel the transmission engaging?
If you put in drive does it act like it is in neutral and rolls?

Got it.
It sounds like the issue with with the shift selector cable. That geos from your gear shifter to the transmission. It could be broken or could have came off of the bracket. So when you put it in drive or reverse it is not selecting the desired gear.
It could just need an adjustment.
In order to access that cable you will have to remove the center console.

I have attached the replacement and adjustment procedure below.
Let me know of any questions.
Thank you.