I wrote an answer to another with this same problem. Perhaps you can find his question on a chainsaw that won't run without the choke. The problem is likely that you put the scooter away without draining the fuel from the tank and the carburetor. The fuel dried out, leaving behind a varnish like residue that has plugged the jets. The carb will have to be cleaned. If you are a mechanical type, you might remove the float bowl and any jets/adjustment needles you see, then using an automotive type spray carb cleaner, blast them vigorously. Wait 15-20 minutes and repeat.
Clean the remaining carb cleaner out with a rag, reassemble the carb and if you have done it right the motor should run.
Be careful with the carb cleaner and follow directions on the can. It will destroy some plastics, cause rubber to expand hugely and can burn your skin and eyes.
This is a very common problem with infrequently used home tools that use an engine. There are some fuel stabilizers that will extend the gas usefulness for months and may be helpful. Sta-Bil is one that I use.
If you are not successful, take the bike (I'm presuming it's a bike) to a dealer. Husky makes many products that could be called a "350" however.
If you do this wrong and loose parts or get things backwards, you could end up with an expense far greater than a simple carb cleaning.
Now, remember to drain the fuel from the tank and carb of any small gasoline engine if it will not be run for a number of months. Yes, it's a bit of a hgassle, but effective to keep things running.
You might be shocked at the number of products I purchase cheaply and resell at a huge markup just because of a plugged carb, fouled spark plug, or ignition wiring that has been neglected.
I just bought a Homelite 24 inch chainsaw for $30. It looks like new, but wouldn't run regardless of what the owner did. He thought it was junk. I cleaned the carb and replaced the gas. Ran fine and I sold it for $140. Took me about 20 minutes and one can of spray carb cleaner. Before that was a beautiful Honda 2000 generator. Same thing, but Imade even more.
I hope you are successful.
Cojon.
Cojon, December 2008