When your CD-i player doesn't function anymore it can have a lot of causes, but to rule out if your remote is still functioning CD-i member Omegalfa shared a nice and simple tip. If the arrow on the screen is not moving anymore it could very well be that your CD-i thumbstick doesn't function anymore, possibly because the IR leds are worn out or that there is a loose contact. Omegalfa (paraphrased): "For the remote, you can use your android camera or other camera to check if the IR is functioning. No need to use the CD-i player to watch the arrow moving. Just point the IR to the camera, press any buttons and verify if you see on the phone or camera a flashing light coming from the LEDs." - You can actually use this trick to test all kinds of remotes."
[Thanks, Omegalfa]