Step-by-step instructions for returns and warranty replacements | Official Roku Support
When you're asked for a serial number, it wants the serial number of the Roku device, not the serial number of the remote. You can find the serial number of the Roku device under Settings->System->About.
You might also want to contact support at https://support.roku.com/contactus since they've been known to send out a new remote, but I think it's hit or miss.
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