Have you checked the cable at the twist grip end ? I'm guessing you have so my guess would be that the carb needs stripping & cleaning thoroughly. ticking over is one thing but any one of the jets could be blocked. I'm amazed it even started after 10 years being stood !
Unscrew the slide from the top of the carb to check that twisting the throttle does actually lift it. If yes then it can only be a blocked jet or jets.
I stored a DR350 for a mate which wouldn't run if left for more than 6 months without stripping the carb.
Looks like it only needs a seat cover & 1 side panel to be sorted.
