My radio is trippen

before you press the cd on button keep holding the eject button while you press power on, I know this works for computers etc.

Possible fault in the optical head unit. You can remove and clean the lens eye to have a final word.
If the loading is happening without the dettecction or the rotation of the disc ,this is for a sure a possibility.
I would advice that you remove the set clean up , check on the connectors and reset.
If fault repeats get opinion before changing the head unit.

The following is the owner's manual for your 2004 Dodge Neon:

http://www.dodge.com/en/owners/manuals/index.html?year=2004&nameplate=Neon

P.99 describes how to load discs:

1. Select and press any numbered button without an illuminated light above it.
2. Insert the CD while the light above the chosen button is flashing and the two lights on either side of the slot are illuminated.
3. Upon insertion, the CD will begin to play, and both the button light and the lights in the corner of the loading slot will illuminate.
4. Repeat the process for loading any additional CDs. The CD playe rwill stop while additional CDs are loaded.

Playing Discs
The radio will show the CD number, the CD track number, and the Track Time Elapsed while the radio is in the CD mode. IF more than one CD is loaded in the changer, the changer will automatically play the next disc after playing the last track of the current disc.

Wow, that's a lot of typing.
I didn't know the 2004 Dodge Neon had such a nice changer.
Good luck.

What happens if you turn the VOLUME to MAXIMUM?

If still no sound , then suspect problem with the speaker , connections or wiring

If loud hissing etc. then speakers appear OK so suspect a radio fault

Hi! I am experiencing the same thing! Have you find any solution? Thank you!

sounds like a bad radio that shouldnt happen bttery has no effect on changer opperation if the radio powers up the changer should work as long as its a factory radio w an internal six disc changer.

dont replace this only needs reset look for reset button?

Unfortunately most times with these 6-disc systems once it quits working it is usually time for a new unit. The manufacturers all reccomend reprogramming the radio, but this rarely does anything other than waste your time and money. Go for the new radio.

TRY REMOVING THE RADIO FUSE & WAIT A WHILE. IT SHOULD RESET WHEN PLUGGING THE FUSE BACK IN.