You may be right, I read a post somewhere that said the 2000 and newer Neons don't use an Egr system and I can't find any info. in my Haynes for 2000-2003 Neon EGR. Sorry for the bad info I made the assumption the newer Neons still had a EGR system.

Have you checked for a Vacuum leak? That could also cause hard starts and rough idle. Also a treatment of injector cleaner certainly wouldn't do any harm.

 

Is the check engine light on? If so then the easiest way to check it is to do this:
1. Put the key in the ignition, dont turn it
2. With quick motions, turn the key in the on position, off position, on positon, off positon, and finally on positon.
The check engine light will not come on for about five seconds, then start flashing. Pay attention to the flashing for example, if it is a code 12 It will flash once, long pause, then twice. It really sounds like to me that it is your cam positioning sensor. Also if you can drive it to auto zone they will hook up their OBD II scanner for free and they will tell you what is wrong. GOOD LUCK