Ignition coil & air/fuel ratio sensor

Hi folks,



Okay, my story is that just yesterday I had my battery (~5 years old) replaced by AAA. They told me I had a dying/dead cell. Immediately afterwards, my check engine light came on. I took it to a local shop, and the dread codes claim I need a new ignition coil (& wires & plugs) as well as a new air/fuel ratio sensor.



My question is threefold:



1) How critical are these systems? My guess is both are critical, I just want to check with the amatexperts.



2) Is ~$670 a decent price for parts and labor for both fixes? That seems a bit on the high side (~430 parts, ~240 labor.)



3) Could either of these have been caused/aggravated by replacing a battery? (i.e. could they have been damaged in the battery install, or would a new battery cause these to fail anyways.)



Any advice is much appreciated, and thanks!



Codes don’t “claim” directly that some particular part is bad.

The coincidence with changing the battery plus more than one code coming on at the same time make me doubt that those parts are bad.

I would only agree to that repair if the mechanic put in writing they would reimburse the cost of the new coil, wires and most of the labor, plus reinstall the old coil and wires if the problem isn’t fixed.

Next thing I would do, if it hasn’t been done already, is reset the computer and see if the check engine light comes on again.

It could be the computer was damaged.