If it's been sitting for two years, the carb is probably gunked up (a common thing with GZs) Try some carb cleaner in the petrol. If that doesn't work you'll probably have to pull the carb and clean it manually. When you do get it running, remember to put a dose of carb cleaner in the tank every three or four fillups. When you get a new battery, no matter what the salesman says about it being good to go, charge it up over night at around 0.75 amps (and certainly no more than 2 amps) Folks who've failed to do this have found that the battery doesn't last very long before they have to buy another. Hope you get it up and running soon.
Just noticed - you said you'd cleaned "crab" thought the typo meant "crap" then just realised you meant "carb". Looks like you may have to do this again.