The answer
The coins stay on the blockchain; a broken display does not itself erase the keys. Do not approve a transaction you cannot verify on a trusted screen.
What to do next
Check your backup is correct using a safe recovery-check method; use a supported replacement device rather than blind-signing.
Trezor hardware wallets
Hardware wallet related to device/backup security; not a guarantee of recovery or anonymity. Availability, supported assets and local eligibility must be checked before signing up or buying.
Visit Trezor hardware wallets ↗Official provider link · Compare suitability and availability before choosing.