Sorry to hear about your thermostat but thanks for reaching out.
What specific Nest thermostat do you have? If it is the newest one with a mirrored display, have you tried changing the batteries? If it's the Nest Learning Thermostat or the Nest Thermostat E, you might want to try charging the display via USB cable. Here's a guide: https://goo.gle/2JgQEwI
Keep me posted.