Check the battery to see that it is working if the generator will not turn over.
Check the fuses. Make sure you don't have a blown fuse and that all the wires are tight and are making good connections.
Check the voltage on the battery or converter to see if it is high enough. This is most important if the generator will not start. Also check the battery cables to see that everything is connected properly.
Look at how much gas is in the gas tank. If the tank is empty it may not turn over. Also check to see if the carburetor is clogged from not using the generator. You should run it for at least an hour each month to keep it maintained.
Check the oil pressure if the generator starts but doesn't run. If it is too low it may not run. Discovering a low pressure may help you find a leak as well, saving you from further problems.
Check the spark plugs. If these are bad the generator may malfunction. Also check to see that the choke linkage is not stuck and that you have a clean air filter.