To start...I am an idiot. Replaced the linkage bushing in our 05 Dodge Neon SXT 2.0l yesterday. So happy that all was fixed I just threw the battery up there and it reversed polarity for about 5 seconds or so. I saw sparks and realized what I did. I then hooked it back up and the engine cranked and the fuel pump starts and all other electronics worked, lights, radio, horn. I did not see any smoke and all the grounds are working. So as I said it turns just does not start and it smells of unburnt fuel after 5 seconds of cranking. Where do I start I think the PCM/ECU got fried .
Any thoughts are appreciated.
And any comments about what an idiot I am can be left out. A. I have beat myself up about this for a day and B. We all make quick dumb mistakes.
Thanks for any help.

What I am going to start with.
Take the PCM to the dealer and try to get some help there, probably just lose money.

 

Update...Bought and installed the following
Battery
Crank PS
Cam PS
PCM.....This one was installed and did the same as the old pcm just threw out a p0513
double checked the relays and fuses everything was good.
Reinstalled the old PCM which still does not throw out any codes just the doNE

The car cranks well now and it sputters slightly...just seems not be firing.
Please any suggestions would be great.

 

Fixed the issue. Dont know why but it worked.
After doing the above I then felt like I didnt have a spark.
So I blocked checked the plugs and there was no spark.
Then I thought I should use the ground from the battery and not the block.
I then got a spark and the engine started.
Put the plug back in and the car is running just as before.
Trying to figure that one out.
Hope this thread may help someone in the future.