Begin by unscrewing the four recessed screws in the rear of the boombox. They don't seem to be magnetic, and they may not pop out immediately.
Next, you will need to remove the mesh that covers the speakers. Using the flathead screwdriver, start prying near the top or bottom of the mesh, near the center. The 'corners' come up more easily. Once you have part of the mesh pulled out, go around the outside and use indents in the mesh to pry it out. Try not to bend the mesh very much.
There are screws now accessible near the bottom of each side under the mesh, near the center of the boombox. Once you remove these, the faceplate will come right off.
Now you can get to some of the electronic components. Only eight screws separate you from the inside of the boombox. Undo the screws and fix up the inside to your heart's content.