Did you check the idle adjustment and carb synch? Also set the idle mixture screws to 3 turns out as a starting point. Sounds like it could be plugged up idle jets. Not hard to clean, but you'll have to remove the carbs to do it. Also make sure the choke is turning all the way off.
http://www.ducatisuite.com/carbadjust2.jpg
http://www.ducatisuite.com/carbadjust2.jpg