"Burning" is a rather unscientific word for rapid oxidization. I suppose when you are talking about burned hydrogen you are referring to water (H2O) which is in fact hydrogen which has been oxidized.
But to say that water is our only abundant source of hydrogen is far from accurate. It is true that we are running low on economically cheap supplies of many of the preferred hydrogen-carbons like oil and various natural gasses which represent "unburned hydrogen". But we have an incredible amount of a hydrocarbon called COAL and the energy stored in the hydrogen-carbon bond can be released from it in various economical ways. One possibility is the traditional method of burning it. Another is steam reformation which strips off the hydrogen which could be used in a fuel cell and leaves CO2 as a byproduct. Coal reformation is basically the process the Nazis used to turn coal into synthetic gasoline during WWII so it is old technology.
You are correct that to reverse the oxidization (or burning) process for hydrogen that exists as part of the elemental makeup of water requires the input of energy. Most of us probably saw water electrolyzed into hydrogen and oxygen in elementary school. The trick is getting lots of cheap electricity. Some small amount may be supplied by solar but we really need to get serious about building fission reactors and also try to figure out fusion.
I have full confidence we are going to figure it out. The market is a powerful force. In the meantime we should let the market decide if bio-fuels are a good idea by ending the subsidies immediately.