Mercury - Mariner :: 2005 - Something Electrical Is Draining Battery Causing Slow Starts?

Back in November I traded my sports car in for a more practical 2005 Mariner with 50K miles on it. I had noticed a somewhat delayed start during the test drive (at least compared to what I'm used to) and assumed it was the battery. Car drove great and I loved it otherwise so I made the purchase and went on my way. A couple weeks passed and I noticed the issue seemed to be getting worse and the engine took a couple more turns before firing up. I wasn't surprised as most battery issues surface when the cold weather kicks in. I took it to the dealer and they found a leaky battery and replaced it and again I went on my way. Unfortunately the issue was not resolved with the new battery. I didn't give it much thought thinking it was just the way the vehicle ran until the weather started getting progressively colder and my delayed start became even more prolonged. So back to the service department I go and wait patiently in the lobby with my book, hoping for good news. When they come back to me 2 hrs later they tell me that something is drawing too much power from my battery causing it to drain (alternator is fine) and they need to power everything down for a few hours and investigate the fuses in hopes of finding the culprit to the power drain. Later on I called for a progress check and they're still stumped and would like to keep the vehicle overnight and see if they can figure out the issue after it sits for a night since (as I relayed) the slow starts are primarily in the morning after the car has sat. From what I gathered, the evidence of drain "disappeared" after a while during their little power down session.

Consequently, I have them investigating 2 other issues and I'm wondering if any of them may be related. One- I am having issues depressing the shift button to get the vehicle out of park (also more of a problem in the morning during the first start). Two- on occasion my key sticks in the lock cylinder when I shut off the engine and try to pull the key out. I spent some time online researching all of the above and it seems that there could be some issue with the ignition switch or a bad solenoid somewhere in the circuit... then again, maybe not? The only other bits of info I can offer since owning the vehicle are that I was having some issue with the rear hatch door. I kept getting the "door ajar" light after using the back hatch.. but I'm pretty sure that was due to my own stupidity because the main door release and the top window release are right next to each other and I may have pressed the wrong one- slamming the back hatch hard took care of the light. The other thing is I followed the manual instructions and deactivated the seat belt alarms because I can't stand the seat belt reminder beeping at me when I forget my seatbelt.