You're a reasonable guy, so its worth explaining in detail.
What you're describing is a breakthrough in desalinization processes, not a re-writing of the 1st and 2nd Laws of Thermodynamics.
Hydrogen "burning" is fundamentally constrained since the only large source of hydrogen we have is water. So, to get hydrogen "fuel," you have to break its bond with oxygen, which requires energy. Great, now we have our fuel. You put it in your tank, your engine mixes it with air, compresses it, and ignites it so that it reacts with the oxygen in the air. What do you have now?
Water. The same molecule you started with.
The energy balance is constrained by the 1st and 2nd Law of Thermo. It took you more energy to separate the hydrogen from the oxygen than you could ever produce by reacting it with oxygen. thackney is being kind by approximating the losses at 30%. It will be in reality a massive loss of energy, due to the inefficiencies of compressing the "fuel" to a useful volume and the horrendous thermodynamic efficiency of even the best internal combustion engines available today. Even the most advanced gas and steam combined-cycle turbine system available today is, at best, 60% efficient. Your car's engine is a wasteful pig in comparison.
These are fundamental laws, not open for debate. Trying to design a process that somehow circumvents these facts is a fool's errand.
Hydrogen = a battery. It would be far more efficient to simply use the electrical energy you started with to power electric cars.
Perhaps I’m as dense as a stack of bricks, but I still do not understand how it cost more than $3.00 to make a gallon (a comparable measure to a gallon of gas) of hydrogen.
What does it cost ot make that gallon of hydrogen? Is it $10, $25, $50, still higher? If you were to tell me that it cost more than $1 worth of electricity, I’d be surprised, but not being a physicist or associated with that industry, I have no idea what it actually costs.
Give me some idea what it actually costs to make the gallon of hydrogen.
BTW, I am familiar with the process of splitting hydrogen out and it joining with the oxygen again upon burning. To me that is the beauty of it. You don’t have to mess with batteries.