Same power cord. And I just reversed the hot and neutral leads on the plug on the power cord - reverse polarity light is still on, but all the 110v circuits, including the battery charger, seem to be working. I am fairly bewildered here...I guess if the 110v circuits are working, it really doesn't matter much if the reverse polarity light stays on?
Please take your problem seriously.
If your power cord was correct before, I suspect you may not fully understand AC circuitry. When you changed the polarity on your power cord, the hot circuit from your house now travels through your mis-wired power cord to your AC panel through the neutral side. The 110vac circuits will still work, you can still use breakers to shut off your circuit and your breakers will still trip. However, you still have a major problem. Even if your breaker were to trip (remember, now it will trip on the neutral side), your hot line will burn up if you develop a short between the hot and ground = fire!
My appreciation for all of this originated from an incident thirty years ago when a friend of mine put a new power cord on a drill with a metal housing. He thought it didn't matter whether the neutral and ground wires were reversed. He was barefooted when he pressed the trigger and was electrocuted! He originally thought the drill was malfunctioning because it needed a new cord. He did not know there was a short in his drill motor. So, when he pressed the trigger, the electricity went to the metal case (which was now the neutral leg) and he was electrocuted.
Similar caution should be made when there is a reversal of the hot and neutral legs ("reverse polarity"). When your Honda generator also indicated reverse polarity, it should have should have put up a flag. When you reversed the wires on your power cord and it did not resolve the problem, it should have put up a flag. It should have been a simple matter to check the continuity from one end of the power cord to the other, in the proper location, to determin if the problem was your power cord. Reversing hot and neutral wires on the plug end instead of checking with a continuity tester indicates to me that you may not fully understand an AC circuit. Although I applaud your desire to fix things yourself, get someone to give you on-site training first.
My reply here is not to insult or trouble shoot through the internet, but to convince you that that are so many things to consider. Unless you fully understand the relationship of all three legs on an AC circuit, it can be a deadly mistake to think everything must be okay if your 110vac circuits are working. What others are trying help you with may not register the same to you and you may trouble shoot opposite of what was intended. Please have a qualified person trouble shoot the system for you and learn from him.