My transmission is stuck in park?

Your fuse for this is in the panel under the rear seat on the left side. there is also a relay there that activates the shift interlock. Here is a guide with the fuse locations below.

https://www.2carpros.com/articles/how-to-check-a-car-fuse

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

Most common fault is the shift interlock solenoid that is part of the shifter.

It shouldn't blow after jump starting unless there was a wire that has rubbed through. Relays can go bad anytime but those are the easiest and cheapest things to do first.

Check ignition 3 relay in left rear fuse block and the rear integration module-

See below

Hello,

This is a common problem. What happens is there is a bushing on the shift linkage that goes out not allowing the shifter to fully engage the transmission and ignition interlock system. Here is a guide to help fix it. Check out the diagrams (below). Please let us know what you find.

Hello,

I'm Tom I will give you a hand. Sounds to me like the linkage on the transmission has come off. Has anyone done work on the car lately? Give me a second I will get the info for where you should look. Here is the linkage spot. Let me get a clearer picture though. You are saying it's in drive only. No Reverse, no Park, but you were able to start it by moving the shifter into park to engage the starter but when it started it was in Drive? The linkage could be bad at the shifter also.
Tom

Hi,

Yes, it thinks it's in drive. Are you able to get under the car to look at the linkage? I think that where we need to start.
Let me know.
Tom

Huey,

Yes on the reconnect or install of the cable. The reverse light coming on when all is done is how you will make sure its adjustment is correct, the indicator on"R", transmission in its second position, light on (REV) will get you to the spot to tighten the adjuster. Then test to make sure its all good
I would put the selector into what you believe is in Drive then slowly move it through all of them counting the clicks or selections making they are all there, see if you can notice if the reverse lights come on, see if the cable coming in is loose. That's what we are looking for under there. Linkage cables don't really break unless it was ever crashed. they get messed up at the ends where they connect. Either the spot that holds the casing solid or the cable end and connects to its lever. We are looking at the same type of thing on the shifter in the console as well. The center console shifter if accidentally hit hard enough could cause this issue. I attached link to a general article for a related part to give you an idea of what is down there at the linkage on the transmission
https://www.2carpros.com/articles/how-a-neutral-safety-switch-works
Tom