I used to fix this all the time for customers in an auto repair shop, and I have this problem with a Taurus I currently own.
Believe it or not, this method works more often than not (assuming your cd player works perfectly fine otherwise):
a) get yourself a CD you don't care about (just to be safe--this method, if performed correctly, won't harm any CD in any way);
b) insert this CD about half-way inside the player where your other CD is stuck while pushing the "Eject" button.
It might take some finagling and a few tries, but BOTH discs should be ejected with this method. That is, as I said above, there is nothing actually wrong with the player itself. This includes your player displaying a code such as "Err" or "Er" or "NO DISC" or some such error (there's a million of 'em, and every carmaker/stereo manufacturer has their own variety). Generally, you can often reset the code by simply turning the ignition off for a few seconds and turning it back on again, but you may need to actually pull a fuse to disconnect the power to the CD player in some cases.
So, good luck with removing the disc--of course, as your Toyota has a carousel player, that does make this all that much more difficult . . . obviously, you'll need to be able to line up the CD on the carousel with the slot where it can be ejected, so if the carousel will not move you're outta luck.
Bob Roberts, April 2009
