I'm not sure which parts contributed to stopping the disk from ejecting, so I'll say everything I did, even if some parts aren't necessary.
I used a KAO disk, but all of them should work.
Look at the sides and bottom of the disk closely - yep, you can open them! As carefully as you can, open the sides and bottom so that the top is still connected. At this point, the metallic thing at the top of the disk should have popped off. If not, well, pop it off! There'll be a little metallic pin thing on the top of the disk that you just revealed. Pull it out if it isn't already out. If a little plastic piece from the bottom-right of the disk falls out(the one that locks the disk), that's ok, you don't need it. Now, open the disk(just fold it open, make sure you don't break the top). See the actual disc inside? It will be surrounded by these foamy strips. Put some glue on the tape part of the disk(most glues should work, I used regular school glue from a bottle). This will stop the disk from turning or revealing data. Now, close the disk and keep it closed, I used scotch tape on the sides and bottom. Wait the appropriate time for the glue to dry, and voila, you've got an unejectable disk. On most systems, you won't be able to take it out by hand, but my computer teacher used this weird fork thing.