I've 2005 Suzuki Boulevard C50T but when start, it doesn't move when I put it on gear. It even goes off when I try to raise the clutch.
I thought about this, but doesn't it kill the engine as soon as you put it in gear with the stand down, even if the clutch is pulled in?If you release the clutch with the bike in gear and the engine running and the sidestand down, it will cut off. This is because there is a safety switch that prevents you riding off with the stand down.
If this is what's happening it is normal; if not, it may be that the safety switch is defective.