Sign in at account.microsoft.com/devices/select-device-for-repair with the Microsoft account linked to your Surface/Type Cover.
If the Type Cover shows up under your devices, select it and choose Start a service order (or Start order).
If it's not listed, click Don't see your device? to register it first, then continue.
Select Accessory as the issue type (since it's the Type Cover, not the tablet itself).
Since your Type Cover isn't responding after all troubleshooting, this is likely a hardware failure and you'll need to submit a service order — the sign-in and device selection flow is exactly for this.
Add a brief note describing what you've already tried.
Review the order details on the summary page and select Submit your request.