This sounds like an electronic fault, I suspect the only remedy will be to send it back to Marklin.
However there are a couple of questions to ask first ...
Does the stop bar light up when powered on? It normally does some flashing while the system boots up.
Does the display light up?
Does it get as far as showing the progress bar on the display as it boots up?

There is the possibility of a bad solder joint on the power connector. Does wriggling the connector change how long it takes to power up. Once it is powered up does wriggling the power connector change the display.

There is also the possibility that the problem is the power supply. Have you tried it with another power supply?
This is probably the more likely problem than the above items, and I would suggest trying another power supply first.

Hi Roland

I have two CS2 and one of them is now refusing to start: the start screen is displayed and the progress bar, instead of stopping near the middle is going all the way and nothing happens.
It happened to me before and I got out by trying many many times to start it near my internet box and when the start was successful I had it call for an update.
It solved the problem for a few month but now it refuses to start.
I know many CS2 are dying that way and no one in Germany seems to have answers.
PS my other CS2 is working fine EXCEPT both the main and programming track outputs are dead.
To be honest this is after 10 years of good service. I have now a CS3

Send the CS2 to Germany? I checked, Märklin does not repair them but offer a "discount" for the purchase of a CS3.
The discount in question is less than ordering from a German shop and having it sent to France so I ordered from MSL (Lippe)
Cheers
Jean

I was thinking about this the other day (after I made my posting above) and I suspect the NAND FLASH chip used for the 'disk drive' is getting excessive errors. While there is a certain amount of spare space in the chip to counter this happening, along with an error correction process, i think the chip just gets too many errors for the system to be able to boot reliably. Sadly the only way to correct this problem will be to replace the chip, but then the problem is how to load the program image onto the chip (it is not as simple as doing another update, which relies on already having a program image on the chip).

The process is similar to when a PC gets disk errors.

You are probably spot on.
have experienced "similar" failures with other types of systems/instruments, where the flash drive fails. sometimes even quite premature, at and of course at the worst possible timing.