I'm not sure if you can see down the throats in a GS, but normally normally you can see a fuel mist inside the carbs. As a friendlier starting alternative, normally you can fire engines on propane. Start the bike cranking and then stick an unlit torch (with the fuel wide open) into the airbox. I wouldn't rev it up with this setup, but you may be able to let it idle until it gets up to temp. Sometimes getting it warmed up is enough to get things going the first time. My guess would be some sort of electrical issue (or an air leak somewhere around the carbs).
Good luck.
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