Same problem can occur in the 2003 - 2008 model XJ6/8 (X350 model).  Captain Morgan's repair works for that model too.  I had the frustrating "CD Fault" message and found a CD was jammed half way across (so couldn't remove the cassette box either).  Remove carpet, remove CD changer (you need a short Torx screwdriver), remove power and optical fibre connections from rear, then carefully disassemble the box, once you have it in a clean environment.  Move the gears that wind the various parts in and out, up and down, to ensure they're free, then apply white grease sparingly with a Q-Tip/Cotton Bud.  Keep the grease and cotton bud clear of the disk drive wheel and laser/reader.  Like Cap'n M says, check it works before reassembling everything.  One note:  Do take care with the connection tape that connects the main box to the optic fibre unit - it is very flimsy and you don't want to break it.
Thank you Cap'n.  Saved £120 ($???) on a repair or £670 on a new box.
                
 Alan Cartwright (England)
                
 November 2009