Why is my transmission not shifting from drive to reverse and/or park?

I bought a '01 Prelude, with a f20b swap on it with about 50k miles, and 135k on the body, and everything is bone stock.

I took it to deq and when I tried to shift it into park, it wasn't budging and the highest it'll go is neutral. So I turned off my engine with the car in neutral and shifted the car into park with the car off as well.

I tried to start it again and it would not start (no crank, no start) so I got new battery terminals and a new starter and I thought everything is okay. Until it started happening again...

Every time my car is like this I have to wait close to half an hour before I can start it again. By the way the headlights are bright and all the dash lights and radio are still on, but when I try to start it, my aftermarket radio seems to fade/die. I have no clue what it is and haven't found anything online like this so I guess mine is the first case. Any advice/ help would be great.