Q: Car starts extremely slowly

Recently I purchased a used car and of course I test drove it and it was starting just fine. The next day, it started extremely slowly. I don’t have to crank it multiple times, but it’s just Very s-l-o-w. (When I turn on the car, an electric motor sound starts, but it turned out to be a broken antenna.) Once it is finally started, it performs very well. A bit about the previous owner: when I purchased the car, I didn’t know that he was a car dealer, because we were at his house. The car had a very new battery (or at least it looks new). The voltage was good according to the gauges. Aside from that problem, my driver’s side window makes a ripping and tearing kind of noise when it rolls up. Also, it will only roll down ¼ of the way. What do you suggest I do to solve all these problems?