2001 S-Type 3.0 Jaguar

78,000 miles, bought used in September. Noticed it was sometimes hard to get out of P and put in gear. Then, the gear shifter got stuck in P and would not come out. We broke it trying to force it. Got that replaced for $700+ at dealership and now having the same problem. It has actually always been a little difficult to get out of park at times, before and even since replaced. It's usually when on even a slight incline. The last time, I messed with it for 10 minutes and the shifter finally came out of park, but the car didn't. I pulled the E brake up and then back down and for some reason it went into gear. Maybe a coincidence.
Sometimes when I put it in drive it takes several seconds for it to lock in gear, or I have to mess with the shifter to get it to go in gear. Any ideas on this problem? I have a "very limited" warranty with a few weeks remaining so i'm trying to have an idea before I take it in. It did not cover the gear shifter before, but I think it covers the transmission. Thanks for any help!