Does it run fine until you open up the throttle? Sounds like the carb needs a good cleaning, improper mixture can jam up the jet with gunk. Those chinabikes usually use a monojet carb thats Easily blockedGet it running and spray Carb Cleaner slowly around the Intake manifold.. (That plastic thing you said was smashed).. If it dies, try again in the same spot.. If it dies again you have a manifold problem. Crack or Gasket..
If it stays alive, take out the reeds (under the Intake manifold) hold a light behind it see if you see any light around the reed flaps..
Could be your Clutch also.. Maybe its dead?
Did you see if the carb was tight like cam said?