Just to try and narrow the problem, I'll ramble a little. As I understand the problem, the engine runs rough when hot, as well as cold. The O2 sensors are bypassed when the engine is cold, this is referred to as "open loop"; in this mode, the PCM provides air/fuel mixtures from a fuel map. When the engine is hot, the PCM switches to the data provided by the front O2 sensors (closed loop). Therefore, (IMO) the engine should only run rough when hot, if the front O2 sensors were bad. The rear O2 sensors monitor the condition of the cat (as some one said). If running rough, and no power, all of the time, the cat may be to blame. I only had one cat go bad (so my experience is far from anything but informative). In my case, the engine would idle fine (hot or cold), but would lose power as the gas was applied. The engine would also rattle (sounded like spark knock). The cat was plugged, a new one solved the problem.