If the petrol doesn't come through first check that you have enough in the tank. If the tank is not full enough it won't come through. If it still fails to come through it's likely that the generator is blocked. This is the tube which the mantle sits on and it has a very narrow opening to force the petrol to convert to vapour when it's warm. Try heating it for a while and it may clear it. Otherwise you'll need to buy a new generator.
Note: while the dual fuel lanterns can burn petrol you should be aware that it gives off poisonous fumes, like cars did before they had catalytic converters. The lantern should not be used indoors with petrol. They are safe with coleman fuel. If you live in the USA, Coleman fuel is cheap but if you're in Europe it's much too expensive. Rather than buying a new generator, if you live in Europe, you could buy a parafin burning lantern like the Petromax 500 available from http://www.pelam.de/index.php?cPath=28_31&language=en&gclid=CIOe46DQnqYCFQkf4QodQxz2Zg
and other sites, or you can pick up second hand Optimus lanterns on Ebay. Both burn parafin, though they need to be primed, and provide at least as much light as the Coleman.