First thing I'd check is the tightness of the battery terminals. Then, I'd check all ground wires and connectors that attach to the body, or engine. Also, what year is your HR-V? Some of the earlier models sold in the US that have push button start, had the contacts inside the push button ignition switch go bad. (They get badly oxidized) This will cause all kinds of wacky electrical issues, such as "no start" issues, door locking issues, engine cutting out while driving, and more. Honda released a TSB (Technical Service Bulletin) to their dealerships about this issue, and I believe they will replace the faulty switch for free.Started when original battery died, possibly from cabin light left on. Replaced battery with a new one, and symptom happened. Charged original battery, and started car, when shut it off symptom also happened with original battery. Any suggestions appreciated.