Wish I had an answer for ya on that one. I've never worked with a Neon stock radio. Rather, only just long enough to take it out and fit the aftermarket replacement.
At this point, it may be easier for you to get an aftermarket radio (more power, features, etc), and the proper mounting brackets. I've seen sets as low as 75 that I would consider worth it. MP3-CD player, with aux in for whatever other source you want.

It may be difficult to find a good working stock radio, since the car is about 15yr old already.

 

Hate to bump this, but it seems you never got an full answer.

To answer your question, for the radio to fit, it must be out of a 1995-2000 Avenger, Sebring, or Stratus. You will notice these stereos actually light up an Amber color. They fit differently, as you noticed, because of the tabs. However, the other stereos should have worked because the plug-ins are the same. I put an "Amber" set in my 1994 Dakota, cut it to fit and everything. Worked great.

I'd suggest, at this point, you check your wiring. If it all checks out, go to the speakers. If they check out, go Aftermarket. Normally, Best Buy has an Alpine stereo, with iPod USB hookup, for 100. It's a little bit more than a JY unit, but you know its in good working condition. The wiring is simple, if you buy the kits it should be 8 dollars or so for the wiring harness, and 12 to 15 for the surround. All the wires are color coated and have directions.

Hope I helped ya out.

 

Thanks for the reply and help. I brought back the second bad unit (to the second junkyard) and he took it back no problem. He called over one of his guys and asked him if they had any more, sure enough a Town and Country had just come in. He brought me to the Van and let me try the stereo out before he pulled it. It was an AM/FM/Cass/CD unit. It worked fine and I bought it for $50 ($10 more for the CD unit).

I cut the tab off with a fine tooth hacksaw blade and it fit perfectly. Everything works fine and my daughter picked up a cheap Ipod to Cassette adapter. That chapter is closed and I'm focusing on a few other projects already! It's funny to see that the last post was a month ago, and think of all the work I managed to get done on my other cars!

-Ken
(for anyone who was wondering:
Bought and installed a battery for my 1972 Volvo 1800ES (google it) which is in primer awaiting an Engine swap and paint)
Bought and replaced the passenger side mirror that my daughter knocked off the Stratus ($35 from eBay and a lesson learned)
Moved my ES out and cleaned up the garage a bit
Cleaned out the shed and organized it better to hold more 'stuff' from the garage
Bought an engine hoist and finally yanked the short block from my parts car (which is sitting in the other bay of my 2-car garage)
Dropped the transmission from the parts car (4spd man, with electric OD (5th spd)
Made 4 calls to my engine rebuilder to find out what is going on with my engine! (again, was promised it by the end of the month)
Got a engine stand from my buddy, stripped it to bare metal and painted it.
Fixed the runs-rich-as-a-b!tch problem with my 1988 Jetta
Of course, that's just most of the car related stuff. Forget about 4th of July parties, etc...
It's been a good month. I'm looking forward to pulling the windshield and dash from the parts car as practice for my good car this week.)