codes would not cause the running problems you are having. You could just have a bad gas cap or stuck EVAP
vent valve for those codes.
Yes, if a coil(s) were bad you should get a steady misfire code. But i have seen on other cars were an entire bank is dead, so its running on half the cylinders, will not give any misfire codes. I think because it is running so bad that the computer cannot determine which ones(s) are misfiring.
With it have absolutely no power, it almost does sound like it is misfiring on one bank. Acceleration causes a heavy load on ignition and that is usually were the problem is. Slow accel may not be enough to get a coil to break down. Maybe the slight stutter and misfire codes were the beginning of one or more coils going bad. I would check all the coils. If you can get it to idle ok, try spraying water on all of them. A lot of times this will cause a coil to fail.