I am sorry for the delay in reaching your question.
The bot***** *****ne here is going to be that you need to have the radio mechanism serviced/replaced, that is what it is ultimately going to come down to. There is nothing external to the radio mechanism that is going to cause this sort of behavior, and there is nothing internal to it that is end-user serviceable (or even dealer-serviceable for that matter).
The No CD message is a result of either the CD mech is not fully reaching the Park position once the disc is retracted and loaded, or the radio not thinking that the mech is fully parked into position... that's it.
Again since the radios are not self or dealer serviceable, you will find yourself with the option of either replacing the radio, or having the radio repaired by a proper electronics repair shop. Due to the cost of these radios dealers do not even replace them when they fail under warranty... they have them repaired (or exchanged with an already repaired unit, technically) to reduce costs. What I would do would be to call your local dealers and find out where they are sending their radios for warranty repairs and then contact them directly to get a quote.
Generally speaking, most repair shops that do these automotive radio repairs as their primary work load will have a base repair price, typically in the $250US range... this is just a minimum repair charge though, and if for example they find the tray mechanism is bent/damaged and requires replacement, that the laser is damaged/out of adjustment or whatever, these would be additional charges. Depending on the severity of the problem, it can add up... but with factory radios starting around $1000 and going up from there, it is usually worth the repair cost. The alternative would be to try to source a used radio which is usually much more affordable at the risk of it failing down the road too, or an aftermarket radio and losing the fit and finish as well as some functionality of the factory system.
Having the unit professionally repaired is usually the best option in the long run, and some shops will even put very long warranties on the radios after they have repaired them as well.