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Could be just that the screen is dead (Nano S displays tend to fail after several years, but they can be replaced easily and they cost only $4 on aliexpress).
If your ledger can be seen on the connected device list on your computer (or you hear a dong sound on the computer when connecting it), then it is just a bad ledger display issue.
If you cannot see the ledger in the connected devices, try another „data enabled“ cable.
Also note that the ledger recover service is not supported by the nano S so there is absolutely no reason to not update the firmware, as it does not contain the code to support the service.