We were told we were going to get on another bus that would take us to our new plane. By this we were all exhausted, confused, and feeling pretty grungy (most of us had been in the same clothes for a day and half by this point). So we waited once again for a bus. It finally came and we boarded. It drove us to a spot near the terminal where the driver got out and was evidently confused about what happened next. We waited and finally a plane taxied over. We all had to walk up some outdoor stairs with our carry-ons, go through a jet bridge and finally walked on (including the 2nd bus that had more passengers) and took our seats.
We sat and waited, again with no explanation as to what was going on. Finally one of the flight attendants told us we were waiting for more passengers who had gotten separated and that we would be leaving once they got here. About 15 minutes later (by now it was around 7 pm), they showed up and we taxied down the runway and took off (I will say the plane got off very quickly - no waiting for a place in line or anything).
We finally made it to Berlin around 8:45 pm. It was dark when we got there. Luckily all our luggage had arrived as well. I had planned on taking the train or S-Bahn into the city, but I couldn't face dealing with public transport and then having to walk in the dark in unknown neighborhood, so I took a cab. He was extremely friendly and I got to practice my German with him. I finally got to the Adina Apt. Hotel in Hackescher Markt around 9:40 pm, checked in (very nice hote!) and barely got changed to bedclothes before I drifted off to sleep.
My biggest problem with this was not the airplane technical issue. In fact I commend them for coming up with a plane for us, but I was VERY frustrated with the fact that no one told us what was going on or what we were supposed to do. They left a large group of tired and dirty passengers in the terminal with no guidance or knowledge. And since it was a Delta flight (with an Air France leg), I blame Delta. It was a horrible experience and I hope I never have to repeat it.