PCM Sensors not setting

1996 Protege 1.5 5 speed. Bought the car wrecked. 53,000 miles on it and fixed the damage and drove it to work. Halfway to work it overheated. Put water in it and checked the oil- milky. Took it to a garage and they put and used engine in it. Also needed a PCM. They put one in it but I think that they put one in it from a automatic. None of my sensors would set so I can get it passed for inspection. I bought another used PCM, because a new one costs $450, made sure it was out of a 5 speed. It ran better and it idled @ 700 or so instead of 1200 rpms. Still no setting of sensors. Took it to a Mazda dealership and they said I had a bad rear O2 sensor and a "weak" catalytic converter. Put a new rear O2 sensor in it and could tell it was running better. Drove it some more but no sensor is set. This doesn't sound right to me. I have never once had a "check engine light" come on EVER. Shouldn't my sensors set and THEN the code come up for a "weak" or bad converter? This is sort of like a catch-22 isn't it? I have to have a perfectly running car for all of the computers to tell me something is wrong? I wouldn't mind paying $499 for the converter IF it would fix my car BUT it doesn't make much sense to me. And I hate spending money JUST GUESSING. Can you please help?