A new battery that does not charge is indeed a clue that the charging system is not working properly. It is not uncommon to fry a voltage regulator with a spark or reverse voltage. Boosting a weak battery to start is often deadly for electrical components. With such an old bike, you must also CHANGE THE FUSES and check for wire harness corrosion.

You should first check get a Service Manual (such as Clymer) for specific procedure on troubleshooting electrical problems. Changing parts at random will cost you far more than the manual. You have to know your bike because there will not be lots of mechanics that will touch a 30 year old bike, by fear of being unable to find parts for it.

In the worse case, you may have to lift the flywheel to service the alternator which will require a special puller. Once again, without the Service Manual, you can cause a lot of damage by not knowing the proper dismantling procedure.

Good luck !

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There is nothing like riding a Honda MC !