"If your Neon has a tape player, don't play Whitesnake tapes... It will eat them and never give them back..."
Well then there is one good thing about these cars!
This is great advice... and 90 Oldsmobiles are also decent with jumping railroad tracks!
Another add-on to my NGC rant above. Still have the car, and did a little tinkering and actually have track times now.
Well, for starters I gutted the entire car down to the sheet metal. (Seats, console, carpet, insulation, etc...) Basically it's a drivers seat, some pedals, a shifter, and a steering wheel.
I kicked the exhaust out to the driver's side rear of the car before the axle, added a Kirk race header (no cat), O2 sensor defoulers, open air intake (no filter, but a sock), MSD coil and wires, new Champion plugs (stock is the way to go, NGK foul too quickly), motor mount insert, trans shifter bushings, under drive pulley, and a 35 shot dry nitrous kit. Stock internals, stock drivetrain, new tires (Falken Z rated 205/50/15). Still has NGC with no standalone, stock tune.
Well, the car is louder and revs a little quicker. Holds power up in the low 6k range, and doesn't wheel hop as bad anymore. I did do some 1/4 mile runs at Byron and she pulled a 15.03 first run, and a 14.90 second run, then back in the 15's before the clutch got hot. The only reason I pulled a 14 was the massive weight reduction. I eliminated well over 200 lbs. of interior comforts, radio delight, and possible structural steel.
Also, the passenger air bag was taken out, and was used as a wake-up call to the girlfriend who is no longer with me.
All in all, these cars suck for performance. As you can see, I dropped quite a bit of money and a lot of time into her for a low 15 second car. For the money I have in her, I could have easily bought a pre-owned Mustang with some nice goodies. 2003-2005 NGC Neons are a joke; if you want a performance Neon, go for an SRT-4 or late 90's DOHC ACR or R/T.
I know you posted this several years ago, but did you ever find an answer? The same thing happens to my car, and I have an '04.
On Youtube there's a video on how to fix it. It cost me 40 dollars for a used part, and 60 for trans fluid.
I have a 2003 Dodge Neon. At around 110,000 miles the engine blew up. I take very good care of my vehicles oil changes when needed etc. When I got the new engine put in, the problems have just started again. Always something going wrong. My suggestion is don't buy any Dodge vehicles; they are junk.