To Check your codes:

Put the key in and put it to the accessory position and turn it off then repeat that a total of 3 times. The check engine light will start flashing. Count the number of times it comes on and pair it up. For example: If the light flashes 2 times and waits then flashes 1 time, that means a code 21.

11 Timing belt skipped 1 tooth or more from initial learned value, Intermittent loss of either camshaft or crankshaft position sensor, No crank reference signal detected during engine cranking
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12 Direct battery input to PCM was disconnected within the last 50 key-on cycles
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13 No change in MAP from start to run
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14 MAP sensor voltage too low
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15 No vehicle speed sensor signal
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17 Closed loop temp not reached or engine cold too long
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21 02 sensor problem (oxygen sensor), upstream or down stream
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22 Engine coolant temp sensor out of range
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23 Intake air temp sensor out of range
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24 Throttle Position sensor out of range
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25 Idle air control motor circuits, target idle not reached (+/- 200),vacuum leak found
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27 Injector control circuit
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31 Evap purge flow monitor failure or evap solenoid circuit
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32 EGR system failure
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33 A/C clutch relay circuit
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34 Speed control Solenoid circuits
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35 Radiator Fan control relay circuit
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37 Torque converter clutch solenoid CKT or park/neutral switch failure
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41 Generator field not switching properly
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42 Fuel pump relay control ckt, Auto shutdown relay control ckt, No ASD relay output voltage at PCM, Fuel level sending unit volts out of range, Fuel level unit No change over miles
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43 Multiple/ single cylinder misfire
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44 Battery temp sensor volts out of range
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46 Charging system voltage too low
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51 Fuel system lean
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52 Fuel system rich
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53 Internal control failure
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54 No Cam signal at PCM
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55 End of error messages (If you get this only, no errors were found)
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62 PCM failure SRI mile not stored
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63 PCM Failure EEPROM write denied
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64 Catalytic Converter Efficiency Failure
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65 Power steering switch failure

 

Well, learn something new every day. Thanks Th3w01f! So those codes he is getting (12, 55) mean there are no codes other than someone disconnected the battery. So, why is the engine light still on?

 

BTW the only Code I got from an OBDii tool was P0340, which is a bad camshaft position sensor I assume (hopefully not a PCM problem) the car is a bit hard to start, and has a bit of a rough idle, also there has been a few times where it seemed like it jumped some as if it was close to stalling!

 

Another issue I'm having, seen on this thread, is the rear driver side tire.


https://dodgeforum.com/forum/1st-gen-neon/385248-bad-wheel-bearing-hub-rear-driver-side.html

 

Change the oil... High mileage Castrol 5w-30. Replace spark plugs with cheap Champion spark plugs and gap to 0.35.

Rocker arms do tick... Valve lash adjusters are known for it. Neon tick. You can pull the cam and rocker arms off a 99 Neon and it'll go away.
Pull the cam off and see if the lash adjusters are stuck. easier to replace the rocker arm than the lash adjuster. They should be sticking out and push in and pop back out. If they don't... replace them. It doesn't really hurt that it's ticking and you can get thousands of miles out of the head.... it's just that darn ticking noise!

Don't ever let your oil get that dirty again and it'll run until the fossil fuel on the earth is depleted. I swear by Castrol high mileage oil... At Wallymart you can get 5 quarts for $16 and a cheap $4 filter. Change every 4k miles. Even if the oil looks "clean".]

Bluetooth OBDII reader. You can read codes and get live data from your sensors with your phone, tablet or laptop. I just leave it plugged into the OBDII port in my Neon. Always have it and my cell phone with me so it's available if I have to check other peoples cars.