Water heater wont work
The rust on your water heater and the cracking of the top surface is indicative of another problem. 

Your thermostat might be broken, the heating element (where the gas is actually ignited to heat the pan) might be broken. 

Just looking at the unit and the rust and given you have this other issue I will suggest you replace the unit, because if you are not a professional in the industry that can be very dangerous for you. Working with Gas is highly dangerous even for professionals. 

That said the cost of a service person to come look at the issue and the cost of any part to repair the unit you might be looking at $200-$400. For that kind of money you can buy a unit have it installed.

You did not say where in the World you are located so if you are in the United States...

Many states have rebate and credit programs, some local municipalities have rebate and credit programs and lastly even your gas company might even rebate and credit programs, the gas company might even install the unit for free (after all they would not want you to use an electric Water heater for the next 20 years would they ?) 

You might be able to end up with a brand new , highly efficient unit for the price of the servicing to fix your unit.