@Em0421, is someone from Roku asking you for a serial number? In general (or perhaps always) they're interested in the serial number of a Roku device even if there's a problem with the remote. As far as I know, they don't track serial numbers of remotes, so the only place to find it would be on the remote itself. You can find the serial numbers of the Roku devices linked to your account at https://my.roku.com.
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