The P0136 code is for the O2 sensor that checks if Cat Converter is working, Bank 1 sensor 2, computer compares that O2 data with Upstream O2 data(Bank 1 Sensor 1) to make sure Cat is cleaning the exhaust, working, it is most likely a wiring fault or water in connector at the sensor.
This sensor doesn't control fuel mix(lean/rich), just detects if Cat is working or not.
You probably don't have the actual numbers from compression test but we will assume mechanics know what they are doing.
Low compression can be caused by a few things(assuming it is just one cylinder out of the six)
Valve or valve seat problem(3.0l heads in the early 2000's had a recessed exhaust valve seat issue)
Head cracked in cylinder(if seen on compression test it would have caused overheating engine)
Head gasket(if seen on compression test it would have caused overheating engine)
Rocker or cam problem, valve not closing all the way or cam lobe worn down and intake valve isn't opening all the way.
Rings/cylinder wall(rings are a longshot)
If a compression test does show one cylinder is more than 25% less than the others then the next step is a leak down test.
You pump known air pressure into cylinder, like 100psi, then measure how much pressure you are losing in cylinder, say cylinder is holding at 70psi, so you have "30% leak down"
You then put in a tablespoon of oil into cylinder, rotate crank a few revolutions then redo the test.
If cylinder now holds at 90psi you know rings were leaking 20psi, if you are still near 70psi then valves, head or head gasket is the issue.
Most places that sell used engines spin the crank and check compression, not always but if they offer a warranty they often do.
Last edited by RonD; 11-22-2014 at 09:33 AM.