You are referring to the pen itself being broken, not the tip, correct? It is
unlikely that Microsoft will provide warranty coverage for a broken pen
casing, but you can use a phone to contact support and discuss
https://support.microsoft.com/en-us/help/4051701/global-customer-service-phone-numbers
- ask for Surface support. Use the phone numbers listed under For BusinessUsers for your location (these also work for consumers/home users).
The broken casing is most likely the reason for the bad pen performance. Sadly,
you may have to purchase another pen.