Hey, that is the best way to buy a ninja, with gummy carbs! Its a super common problem on these as the passages in the carb are way small and prone to clogging. Sometimes you can do the old 'italian tune up' and ride the piss out of it and get whatever is clogging it to come through, but more often than not you've got to poke them crabs.
I'd check the air leak route first, all clamps are tight and all the boots are secured correctly, lots of crummy moto shops will screw that one up.
Get yourself a big fatty lawnmower fuel filter for it, one of the clear ones so you can see if there is anything coming through.
Worst case pulling the carbs isn't that bad, hardest part is getting the boots back on the airbox. Put the boots in boiling water and they'll get real soft and go on easy.
Time to learn to rebuild a carb, the ninja ones are pretty easy, just don't be a ham-fisted doofus and you'll be fine. Next you can do a Quadrajet, it will make the ninja seem easy.
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