The problem sounds internal and serious. Probably not the starter directly but the gear train the starter drives. There is an idler gear and driven gear with a sprag clutch linking the starter to the crank. The idler gear shaft bushings have been known to fail. If you push start the engine, listen for any weird sounds. Is the bike still under warranty? If you are over on your warranty and the idler bushings are broken, Triumph has been known to still cover on warranty.
Good luck.
