I have over 114k miles on my car and was running good until last week. It is a 5 speed manual transmission and started to make a popping sound when I would shift gears. It also would "pop" when I put it in 1st gear. I read in another forum (Dodge Dakota forum) that someone had the same problem and they suggested to replace the distributor cap and rotor. I'm wondering if it may be my timing belt or other timing problem.

 

The neon doesn't have a distributor cap and rotor. It uses what is called a coil pack to distribute the spark.

What kind of popping sound? Is it a rattle or clicking? At 100,000 miles the timing belt, water pump and idler pulley should all be changed. You don't want the belt snapping and ruining (bending) your valves.