I crossed the battery terminals installing a new battery.

Sounds like the Security Light

https://dashboardsymbols.com/2019/06/warning-lights-and-symbols-seen-in-dodge-vehicles/

https://www.google.com/search?q=2004+dodge+neon+dashboard+warning+lights

..

Try pressing down on the red security light on the dash and hold it down for about 3-5 seconds. Sometimes Neon's just have a dummy light on the dash that isn't actually hooked up to anything, but its a good place to start.

Ok, even if the battery is new, get a voltmeter and measure the battery, if its below 12v, thats the problem. That way you completely eliminate all these factors without a doubt. Also check negative wire from battery to the ground box and connections. It sounds more like a corroded terminal.

try cleaning the terminals, jump starting or use your key to unlock your driver door manually. Perhaps the factory alarm is armed and will prevent the vehicle from starting

Go under the dash and bypass the clutch pedal safety switch and see if it starts.

If you indeed installed the positive battery cable last and the neg first you blew the computer possible, you will need a complete diagnosis.

you have a bad earth issue>>> cross wires or terminals...

be thankful u didnt get burnt or electified-probly just cooked the insulation off the batt cables-ok for a while but keep eye on it like ur preventive maintenance--always double chec between pos n neg specially wen tired or at nite

try replacing the alternator.

look everyone !!! i am not the only one who has this problem , but I found the answer on my own.... iI hope this can help others . If you have to replace a neon engine you must do these thing if you want it to start.
<br>
Lower vehicle and perform camshaft and
crankshaft timing relearn procedure as follows:
² Connect the DRB scan tool to the data link
(diagnostic) connector. This connector is located in
the passenger compartment; at the lower edge of
instrument panel; near the steering column.
² Turn the ignition switch on and access the “miscellaneous”
screen.
² Select “re-learn cam/crank” option and follow
directions on DRB screen

Most people don't have access to this scanner <but it must be done> I used a snap-on cost 3000 but have the reset feature

Thanks you all for your help.