I'll bet the fusable link for your alternator blew when you jump started backwards.
On older cars the fusable link was simply a short 6" long section of a special type wire, on more resent cars like yours its commonly a much larger than normal sized fuse that plugs into an electrical box under the hood. That electrical box will probably also contain regular sized fuses and relays.
The fusable link will be rated to blow at somewhere around 100 +/- amps.
The fusable link i think is your problem here will just have 2 wire connections and probably just plug in.
(but it might be a short section of special wire like older cars instead) 1 of those connections will be wired to the battery's positive post. The other 1 will go to the large B+ output terminal on your alternator. So when this fusable link is blown, the alternator will usually still be charging, but the output cant get back to the battery...
An easy test to confirm if this is your problem, is to see if the big B+ output post of your alternator has battery voltage with the engine off. This output post should read battery voltage at
all times.
And then while the engine is running, also measure the output voltage at the alternator, and then compare that to whats getting back to the battery. You should never have more than a 1 volt drop/difference between those 2 points.
Also, definitely check every single fuse in the car. Jump starting backward may have blown several fuses.
Its also very common to damage the cars ECM (computer) when jump starting backwards. But not always.
I'm not sure what year your Neon is but the voltage regulator for your alternator
might be built into the computer...
Here's some info about that:-->
http://www.batauto.com/Forums/index.php?topic=4166.0
You might research here too:-->
http://www.google.com/search?source...T4GZAZ_enUS369US369&q=dodge+neon+fusable+link