Car sometimes will not start

I was fooling around with it today, tried to crank it, and noticed it wasn't firing. Then all of a sudden it started back firing, but still misfiring on multiple cylinders. For the life of me I can't figure this out. I'm wondering if it's not the crank position sensor, but I really don't have any idea.

A few weeks ago my car started having the door chime go off when you turn the car off and take the key out but when you shut the door it would stop. Also when you tried to start it it was hesitant to start. Just got a new starter today put in. But now the door chimes even when you shut the door and now I think it drained the battery because it wont start, but the exterior lights stayed on.