Have you found the problem yet? I had a disc freeze in the player a couple of days ago. Yesterday I pulled the unit completely out of the dash. (I couldn't get it to do anything with the CD player, eject,play, etc.). I opened it up and removed all 6 CD's. I re-assembled the unit and re-installed it to the car. I got the same thing as you. It didn't even give me the option of the CD mode. I had planned to remove it again today and look for the problem, but when I tried it this morning, IT WAS BACK! I believe the changer has to relocate to an operation mode before it will show up again as usable in the mode switch.
Try this. As you know, you can eject, and reload the CD's with the key off. Leave the key off, and try to eject, and/or reload ALL 6 CD SLOTS, one at a time. Maybe even do this a couple of times, just to get the changer to organize the proper play positions on the stack. If it doesn't work yet, walk away from it. Let it sit overnight. Then try it. I don't know if the changer requires time to initialize, but it's worth the time. Please let me know what you find, one way or the other.
ps: mine is a 2004 also.