The CDX is 20 years old. Can't say that blowing fuses is a "known" problem as mine has functioned perfectly nearly all this time.
Your first clue is the leaking electrolytic! Stop, do not proceed until you've replaced those caps. You can stress the "rest" of the power supply out replacing the fuse and powering the thing back up with a short; notably the regulators could be come damaged.
I don't have the schematics with me at the moment, but you should be able to uncouple the rest of the CD player from the power supply. When you've done that (after you've replaced the electrolytic) try to power it back up to see if the fuse goes. If it does you know the problem is in the power supply. If all is well and the voltages measure up then plug the rest of the electronics back in and try again. Once you've fixed the problem, replace all of the electrolytics especially in the power supply as its probably about time. The CDX runs very very hot and over time the caps get nice and cooked.
A couple of things that you should know about the CDX
1) The glass control panel is glued to the body mostly likely with double sided tape. While mine has held just fine, there is a possibility that the adhesive might be going so when moving the deck/flipping it upside down etc... the glass panel could come out and become damaged. It would be a good idea to tape the glass down just in case.
2) There is a metal rod inside the deck that is responsible for flipping the CD tray up. This rod rests on two very very thin and fragile plastic supports that are molded to the plastic body of the CDX. If not properly aligned, they could snap off. Be very careful!
3) A few years ago my CDX started acting up with intermittent play issues. The problem was traced to cold solder joints. While you have your deck open you may want to spend some time reheating all of the solder joints to make sure things are solid again.
4) Finally while you have the deck open you should apply some lubrication to the gears in the lid mechanism as it is likely dried up. Take care not to get any on the belts otherwise the lid will not open properly due to slippage! (If belt is loose or cracked, now is good time to change.
Derek