Thank you “asemaster”, “mark9207”, “Cigroller” and “EllyEllis” for your replys. I learned that the “black box” on top of the engine with the spark plug wires attached to it (that looks like a “distributor” to a 20th Century guy) is actually the coil assembly, as you say. But I don’t feel bad about my ignorance because I called five autoparts stores and none of them suggested that what I needed was a coil assembly or coil pack. They all just said, “We don’t have any distributors for a 2003 Dodge Neon”. None of them knew enough to tell me that a 2003 Dodge Neon has NO “distributor” (as you guys did). And this is there job … selling parts for cars.
“Cigroller” and “EllyEllis” were right. The problem was ultimately found to be poor compression in the Number 1 Cylinder. When the new coil assembly failed to correct the problem, I took the car to a good mechanic (with lots of positive reviews in the Internet) and that’s what he determined. He thinks the compression problem could be due a problem with the valves, piston rings, or possibly something worse with the cylinder head (?). In any event, it’s going to be big bucks to get if fixed. 