O2 sensor won't make the car not start... doesn't even start reading until a minute or so after the engine actually starts (has to sufficiently heat up).
That being said, downstream (after cat, yes?) is even less of a player, simply monitoring if the cat is doing it's job.
You say it takes 30 mins to an hour to start? Explain.. you just crank it for a half hour, whaaat?
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