Is your 4620 connected to WiFi?
If so, you can use the Roku Remote app to connect to it (assuming its on the same network) and either use the apps "System Info" function with the 4620 select, or Settings/System/About in the Roku's UI to get the Serial # etc.
You can also get the Serial # from the bottom of the device.
If it your Roku isnt connected to WiFi, you'll need a remote to configure it/connect it to WiFi.
For official remotes, either the $15 Simple Remote, $20 Voice Remote (RCAL7R), or $30 Voice Remote Pro (RCS01R) can be used, and can be obtained from Roku.com/Walmart/Best Buy/Amazon/etc.
For unofficial remotes, you'd need an IR-only Universal/Roku pre-programmed remote, which can be had for $5-15 at Walmart/Best Buy/Amazon/etc.