If the Mitsubishi is an old remote, chance are it doesn't have a code for your new CD player, so you will need something to learn from (assuming the Mitsubishi is a learning remote). I would recommend that you take the Mitsubishi down to the store where you bought the CD player (or any store for that matter) and see if they have a display remote that you can learn from.
Failing that, maybe a new universal remote would work the CD player. If you post the brand and model number, we can say what the likelyhood of a universal being able to control it is.
Rob
http://www.hifi-remote.com