Can you remove the piece of broken stem from the crown?
Your crystal may be salvageable. If you work with an 800 grit wet/dry sand paper followed with a 1200 wet/dry sand paper then finally finishing with brasso or Solvo Autosol, you can probably restore it to near new visibility. It could take several hours of hand polishing to achieve this though. A new crystal may be more appropriate unless you have the patience to do the polishing yourself.