First step is make sure you have your clutch pulled in. All Suzukis have to have the clutch pulled in to start. Even in nutreul. A buddy of mine had a Suzuki for a month and forgot about it after not riding a week. He called me saying he was probably going to take it to the dealer. I then told him to pull the clutch in and it worked.

After that with it just "Whinning" i'd say it's something with the starter. Not sure what. Do you have an OHM meter? If so just start hitting some wires and make sure they are connecting.