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Were the replacement parts OEM Honda?
If the stalling started after you replaced the battery try this trick, remove the negative then positive battery cables and then touch them together for 3 mins. at least. Then put the positive then negative battery cable back on the battery and then start the car with the A/C off and let it run without touching the gas pedal for at least 10 mins. If you replaced the battery and didn't let the car run 10 mins. to learn it's idle then you may have a stalling issue.
Try letting it run for 10 mins. to learn it's idle values then it should work if that's the problem. As for as the other codes go the second one is for a bad cat. converter and the first code is for insufficient EGR flow. The first one is most likely a faulty cat. converter and the second is probably coming on because you have a clogged up EGR passage in the intake.
Figure a couple hours labor to clean out the EGR passage and a hour of labor to replace the cat. and about $200 for an aftermarket cat. converter.
Hope that helps.
Get a Honda OEM replacement ignition switch and have it installed. You have the classic ignition switch failure symptoms. The only think I can think of besides that is a bad coil or ICM inside the distributer.
Most of the time you remove the dist. cap and rotor and you take a test light and touch the black/yellow wire while someone cranks the engine over. The test light should be on with the key in the "on" position and flash when the engine is cranking. If you don't have flashing the ICM is bad. If you have flashing and it doesn't start the coil is bad. Easy.