Just to update, I had already had this remote.
But I couldn't figure out how to custom program any buttons. The main button I wanted was the "L" key to cycle subtitles.
So I loaded this program, LM Remote Keymap.
And I was able to find my remote (called a Hana in their system), and I was able to program one of my remote keys (the "*") to be L and cycle subtitles.
I also used this LM Remote Keymap to set one of the buttons to open the application XBMC.exe, and if it's already open, bring it to the foreground.
So now the only thing I still need to do is make sure XBMC opens in fullscreen mode, or if it's already open in windowed mode, for a button to toggle fullscreen. You can do that with a keyboard with the usual ALT-ENTER, or XBMC has a hotkey with the backslash (\) key. But unfortunately I can't seem to get the remote to recognize those fancier keystrokes.
Anyway, I'm closer.
Does anyone know how I can reprogram another regular key, like "F", to toggle fullscreen for XBMC? If I can do that, I'm sure I can get the keymap program to work with an "F".