OBD11, okay.
I found a connector that was not properly seated, and connecting it properly caused the "Service engine soon" light to go out.
However, I'm still getting cutting out and backfiring.
Probably dumb question: when I changed the starter and failed to seat that connector properly, could that have caused something to happen with the onboard computer? Is it possible that reseating the connector now did not undo whatever happened with the computer, and that's why I still have backfiring? Is there a computer reset?