2005 Vibe base model. A bit long winded here. The headlights on my vehicle were left on causing the battery to die, this resulted in the car being jumped. After jumping the vehicle it was driven just fine without issue. The trip post-jump was about 7 miles and a 20 minute city drive. Two days later the car was started and drove incredibly rough, eventually presenting with a flashing check engine, steady VSC, and steady Traction Control light. This continued for the duration of the drive (10 minutes round trip, city), until it was once again returned to its parking spot. When I got a chance to look at it, the codes read from the OBDII were p0171 and p0303. System too lean and cylinder 3c cmisfire respectively.
After surfing the forum I decided to try replacing a spark plug on cylinder3 because I had the parts on hand for it. After replacing the spark plug, it started a little rough but smoothed out in idle. I put it in reverse (still smooth) and pulled out. It was rough while driving for a very short time before presenting with the same light pattern as previously, as well as the same error codes.
Next I tried disconnecting/cleaning the battery for ~20 minutes to reset the ECM (cleaning wasn't necessary but needed to kill 20 minutes). I started the car and let it idle in park, it started out sitting at ~1500 RPM and slowly lowering itself to ~1000RPM within a few minutes. Pretty rough at 1500, pretty smooth at 1000. From here I let to continue to idle and after about 1 minute of smooth idle it started to dip towards 500. Every time it would start to dip and get rough, it would eventually revert back to the sweet spot of ~900. It did this for about 10 minutes, dipping lower and getting rough then reverting and getting smooth. I know after resetting the ECM the vehicle needs to 'relearn' itself, but I stopped because I was concerned 10 minutes was enough time in idle for this to occur. park in an enclosed parking garage (18 cars) and I was concerned about having the car run for much longer in a space with poor ventilation. I also haven't found great documentation on a proper 'relearning' process.
From here, my next two steps are to clean the MAF sensor (will need to relearn again) and replace the intake manifold gasket. My reserve on all of this is the fact that the issue happened almost immediately after dying and being jump started. The likelihood it was jumped and then almost immediately started presenting these issues makes me think this has to do with electrical component and the ECM. Should I allow it to sit in idle longer to be 'retaught'? I don't want to jump to messing with the MAF sensor or replacing a gasket if they have nothing to do with my issue. My second thought is that something occurred during the jumpstart that damaged the ECM or possibly the O2 or MAF sensor.
Not sure if this is relevant to the issue, but the battery is over 3 years old as well. Somewhere near 5 years I believe.
Any insight would be appreciated.