1997 Jaguar XJ6 Turns Over, But Won't Start, Squealing, Hesita

Did I get your attention? Two days ago, my car wouldn't turn over. It sounded like it would, but it never started. I called AAA and they were able to start it up with the help of the portable jumper boost to the battery while pumping the the gas pedal. It finally started with a lot of bluish exhaust. It ran fine until tonight. Same thing. Couldn't get it started, even with a jump. I kept trying to start the car and while it finally turned over and started, it shook for a while, the engine squealed for ten seconds or so and then quieted down. The engine light is now on, too. I waited until the car felt like it was idling smoothly, put it into gear and drove home with no problem. First of all, what does this sound like to you? Secondly, could it be related to two other problems I have been having: hesitation when I go from a stop to moving and an intermittent problem when I am driving on the freeway and let my foot off the gas, it kind of jerks and feels like it is shifting into low on it's own. It only happens sometimes and whenever I have a mechanic in the car to show him, it never does it. The first problem just started this week. I want to get all of these things fixed. Help! Thanks, jeff