It sounds like the carbs are gummed up. They will need to be disassembled and cleaned thoroughly, especially the jets' tiny little holes which gas passes through, to be atomized. There are video links to YouTube on the Home Page, that demonstrate how to do it. The Factory Service Manual (FSM) is also available for download from a link on the Home Page. After you get the carbs cleaned, adjusted, and synchronized, run some
SeaFoam through the tank, to dissolve any varnish within it, as well as absorbing any water that may be lingering at the bottom of it. Run some
SeaFoam through the gas tank once per month, or so, to keep the carbs clean, and water at bay; used as a preventative measure,
SeaFoam will prolong the life, and health, of your carbs, and the bike as a whole.
I'd recommend changing out the fork fluid, and the crankcase oil and filter, soon, as well. The fork tubes use
Dexron III ATF (around $5/quart, nearly everywhere), and changing it will make a nice improvement in the handling. Cheers!
1979 CB750K (sold, 2012, but not forgotten)
1983 Kawasaki 440 LTD Belt Drive (sold, 2011)
1993 Kawasaki Voyager XII