Yes water can store energy, there are currently two commonly known ways how water can store energy. First, one give it force to rise it to higher ground, to use the energy store, just release it, it will flow to lower ground, everthing that have mass will do this! Secondly, split it into hydrogen and oxigen by electrolysis. Then burn it to get back the energy stored!
Picture below show a conceptual idea about a power generator that store solar or wind kinectic energy in the form of potential energy, people have built similar water fall generator but the cost is way too high to built it at sea. The pieces of this generator have to be built on land and assembly it at the shallow sea. Black color retangle show the hole for water out to drive electric generator, and the white color show the hole for water intake with pump, water is pump into the tower and store as potential energy by using the power supply by the solar cell or wind turbine when there are extra energy unused.

According to conservation law of energy, energy can not be created or destroy by human being. We can only store it or convert it!
In our natural, water is a stable sustances, mean that it will not produce energy by it-self. Please note that the different between word 'produce' and 'create'. Create mean from non exist to exist here, produce mean from unseen to be seen!
By using electrolisis, the amount of energy can be stored is actually lower than the amount of energy it required to split the water, some energy will lost as heat!
What happen if we can produce more hydrogen and oxigen with lesser energy? This is not something imposible, but that just do not occur under normal circumstances! The real secret is the catalyst use in the system.
It just similar to uranium do not produce energy by it-self, but with the added of other reactant that produce neutron, it then produce heat!
What is the different between catalyst and reactant? Reactant is something that directly join the response, just like oxigen is reactant to any chemical fuel but not a catalyst. We do know that with existance of catalyst, any chemical response than initailly will occur, will become faster, from undetectable rate to become detectable.
Catalyst is something widely use in China medicine making, there is a say that herbal(s) will not produce it function effectively if lack of some other herbal function as catalyst, but if you use only the catalyst itself it have not particular function at all. Just similar to people add salt to apple or watermelon, the fruits become more delicious after adding salt.
That mean in a water-fueled cell, the catalyst have the most important role there! It can be something that add into the water, or something that built up the electrode.
The problem remain to me is that, even the best catalyst used, let say 100% efficiency of energy used to split the water, it still gonna lost the energy at the output, therefore the energy slowly reduce and eventually the machine stop.
The only reason I can think of, it is not catalyst that playing the role, it is reactant that been used, reactant store the energy needed to split the water effectively.
But please note that reactant is something that can be exhausted! If we consume up all the reactant on the earth, it is similar to the result of comsuming all petroleum!
This reactant do work for a period of time, and then it can die off. There are just no free lunch in the world! You got to pay for it once a while. You can not expect your water fueled cell power you for too many years. Once the reactant wear out, it stop working! Everthing converges! Nothing diverges! That is what make human being can not be seen as 'thing'. Thing that do not converges must have life. And a reactant do not have life I believe.
If the petroleum price is more expansive than the reactant price, then it may be good to use water fueled cell. Otherwise not.
There are currently two type of water fueled cell is claimed have been invented, first type is currently master by advanced country, with the help of catalyst or perhap reactant, they can directly produce electricity, which is the world most efficient water fueled cell. The second type is those spliting water to hydrogen and oxigen, and then burn it back to produce energy. Internal combustion engine will not produce energy with more than 50% energy store inside it since my last access to the related data, may not up to date, you can try to check it out yourself.
There are two main reasons why the water-fueled cell is not so good to use it in internal combustion engine or car. First you need to pay for the reactant, the benefit is actually very hard to be calculated. If the reactant is built into the electrode itself may give you more problem, as the efficency decrease with time untill all the reactant stop functioning, the system will not give you any benefit at all! How many water the system can split bacome the key to how much petrol you can save. It may actually more expansive than the petrol you can save depending on the price of the reactant or the whole system.
Secondly the engine block, piston, valve and any other part involve, must be anti-stain or must have good lubricating system. As a product of combustion hydrogen and oxigen will produce water, will make the internal of the engine rusted more obvious and reduce the life of a car, especialy the exhaust pipe.
And stain can spread, as water is only some sort of catalyst to oxidation, oxigen inside engine block will be suficient to make it rusted and become unususable in months if the car leave unuse, after the lubricating oil become too thin or at the part the oil do not reach. Some say engine block can be make of hi-tech ceramic such as those invented by Kyocera (Tokyo Ceramic), but I have never see it for myself yet.
Therefore, solar energy is still considered the best long term energy for earth currently! A good solar cell will at least function more than 10 years. Untill we can use solar energy to produce reactant for electrolisis, it is not safe to say that water-fueled cell is a good source of energy. And I believe thing that can store or contain large amount of energy, must be radioactive! As the energy will slowly leaking althought the reactant do not exist.