2004 Dodge Intrepid Please Help

My name is Erin. I own a 2004 dodge Intrepid SXT. Well when I first purchase my car in 2008 it actually would jerk and shake when I accelerated on the street or Highway. I had a fuel injection done and it still jerks and shakes some times when I accelerate. What do you think that could be? Because most mechanics I asked dont know. Then a few days after having my car, it kept cutting off at stop signs and street lights and some times it would cut off when I'm driving on the streets or highway. Pretty Dangerous! Now for the pass few weeks I been having to get a battery jump just about everyday. Now the jumps are not working. So I went and got my battery tested before my car started to need a jump everyday and the mechanic told me that I need a new battery. But most places I called about changing my battery tell me that they can not change my battery out because they would have to take my right front tire off to get to the battery. Since the jumps will not work on my car and my car does turn over when I go to start it but it wont start and when I let my car rest and cool off for a while it will eventually start, what do you think could be wrong with my car? Could it be the battery? Could it be a faulty switch? Could it be the start but I dont think it is? Could it be a fuse? Could be my air intake? Could it be the belt? I honestly dont know what it could be. My car was stolen exactly a year ago and I spent the only money I had saved to get another vehicle. So I can get to work and to my classes. I am a Relief Manager at The Ronald McDonald House and a Senior at the University of Alabama at Birmingham. I would really and truly appreciate if you could help me. Thank You So Very Much