From the description of your problem and sequence of events your fuel cutoff solenoids have nothing to do with your problem. It only has 1500 miles on it and it sounds like it has sat for 1 to 2 years. That's what has caused your problem. All it needs is a complete carburetor rebuild by a competent mechanic, preferably at your local Yamaha dealer. The reason I recommend a Yamaha dealer is because they will have access to any of the OE parts, o-rings, etc. that may be needed to refresh them correctly. They should be completely stripped and soaked in a quality carburetor solvent that will desolve all of the dried up sediment left behind from the dried up fuel. After soaking they should be brushed and cleaned with a standard cleaning solvent and carefully blow compressed air through every circuit to completely clear it. It's the only way to be sure everything is thoroughly clean. If it's done shodely with a can of contact cleaner you can do it quicker but chances are high you won't get everything completely clean and will still suffer rough running to some degree. All it takes is a partially colgged pilot fuel delivery circuit on one of the carburetors to make it sputter, backfire, idle rough, not idle at all or run rough in general. All of the newer fuel formulas for the past 3 or more years are much drier than ever before, leaving behind residue and little crusty flakes once it dries up and evaporates. It effectively chokes down every circuit it runs through and you can see the greenish residue in the float bowl, chamber, jet needle and venturi. On top of this you need fresh 87 octane fuel and make sure you have good fuel flow to the carbs. Your Star model will not benefit from higher octane fuel. You'll only be wasting your money. Once you get the carbs clean and it runs well keep them that way by running the motor for about 5 minutes, ONCE A MONTH, during those months that you can't ride. This is normally sufficient without the use of any fuel preserve additives. I hope this steers you correctly. If you have further questions don't hesitate to ask. By the way, the purpose of those fuel solenoids is to shut off the fuel supply if the bike goes on its side.