Is there a vanity cover over the drive? Also, can you press the eject button to close the drive after it has opened, and will it stay shut then?
What model is it? I haven't seen a case I couldn't open...one way or another.
Some case screws will stay in the panel. In other words, you can screw them out slightly, then they catch, and you can't pull them out completely. If this is what your's is doing once they are all out, just slide the panel back (usually). Some Dell's also have a release lever you can pull. In those models there are no screws. Just pull the lever and the side opens up or pops off.