2000 Mitsubishi Mirage multiple problems (starting, smell

2000 Mitsubishi Mirage 4 cyl Four Wheel Drive Automatic

I have a 2000 Mitsubishi Mirage. I've had it for 8 years, and now I'm starting to have some problems. Last year I had to replace my battery and alternator because the care suddenly stopped working one day when I was driving. Since those changes were made, if I let the car sit for 1 day, the next day I try to drive it, it will not start. After I get a jump, the car immediately has a burning rubber smell. As of yesterday, my 'check engine soon' came on and will not go off. I took it to Auto Zone and they ran a diagnostic test and gave me a code. They said it has something to do with my fuel injector trim (or something to that affect). Is there a connection between all of the problems? If anyone can help me, I would greatly appreciate it!