Hello sonavor
I rebuilt my CDX hinge a few years ago but unfortunately, I have been battling with this same problem for quite a while now. About a year ago, I set up all of the limit switches according to the manual and adjusted the lid position using the allen key through the bottom opening - as Olli referred to. Yes, I managed to get the CDX working well for a short while. Since then, I have had two or three occasions where the lid closes but the disc is not read or played. The symptoms are always the same, lid closes, the lid motor runs on for a short time and then nothing happens.
About three weeks ago, I had the last incident so I opened up the unit and checked everything once more. My problem is definitely related to the two way load switch and the solution seems to involve a fine adjustment on the position of the limit switch and using the hex key to set the lid an optimum closing position. The switch contacts can also require a slight cleanup. The bad news once again is that I still cannot get it 100% correct. It works once or twice then stops working. If I sqeeze the lid at the back left corner where the limit switch is and press PLAY at the same time, it often starts to read and plays well.
Yes, I think that the hinge modification has knocked out the various settings by a mm or less and we will have to find a new "sweet spot" for consistent operation. Let me know if you find a guaranteed way of setting this up because I have just about run out of patience on this one. In any event, I have several other CD players that work well so fixing the CDX is not a high priority these days.
Have fun
Regards
Geoff