Several things can be tried.
1. Hard reset. Press power button for 10 seconds and see if that restarts the phone.
2. Hard reset. Press volume + and - buttons for 10 seconds and see if that restarts the phone.
3. Connect phone to computer via USB port and startup BlackBerry Link. See if phone appears as connected. If phone connects, proceed with immediate full backup.
4. Device reload. If while connected, BlackBerry Link cannot connect to phone, select Reload software to restore phone to factory settings.
5. If warranty is expired on phone, try to find an authorized BlackBerry repair centre and send for repair.