Exact same problem that I had when I purchased my ex-police ST1100. The bike had been sitting in the guys front yard outside in the weather for 2yrs. It was in shocking state, windscreen baked opaque by the sun, body plastic broken or missing, never been turned over in those 2yrs. Bought it off him for $300. Stripped the bike down to frame and motor. Refurbished all other parts. Spent about $2000 on parts and many hours of labour. Changed all the fluids and oils on the bike and when it came to running the motor, it ran with a miss in the motor, was only running on 2 cylinders. Had to finally strip down all the carburettors and clean all the jets and bowls. Carefully cleaned it all by hand with solvent and nozzle cleaning wire, careful not to damage the jet orifices. Did find a lot of petrol gum in all the nooks and crannies.
When I put the carbie bank together and back on the engine, I still had a rough idle and lacking power. After using 3 tanks of petrol with carbie jet cleaner without much success, pulled the carbies off again and found the rubber sleeves between the carbies and engine block were not sealing due to being hardened. Did not realise how hard they had got until I purchased a new set which were very flexible. Fitted the new sleeves and, presto, good idle, plenty of power and all cylinders firing.
Hope this helps,
Cheers,
Hobs