car suddenly wont start - never ran great anyway, esp. cold, now cranks, but won't st

[rjSupra]

Thanks for the explanations Cre. Before getting this car I have to admit I really did not know what an Oxy sensor was, what it looked like, and what it did - in any car let alone this one. Sorry for the newb-ness.
I did pull my CPS to repair the coolant problem before and very carefully set it back in correctly aligned the way it was supposed to be (TSRM) with the crank at TDC both visually on the pulley. So that part of the ignition is in spec.
(in also ran identically to how it ran before I pulled it out).
I have not gone any further than finding the two transmission code problems so far. Have not been around the car for several days and have not put the volt meter to different parts / wiring yet.
My car is not having knock problems, nor is it mis - firing. Although today for the first time after starting it and it was idling fine for 2-3 minutes, it did stumble heavily once during idle and then ran normal after that. (like the motor sounded like it was bogging down and like it would almost stop running for a few seconds and then went back to normal idling about 600 rpms like nothing had happened).

You might be right about the mechanic guy - could be either one of those types you suggested.