From experience, there are several possible causes for the failure you describe. Unless you have the skills required to diagnose and identify the exact faulty part you may end up buying parts you don't need until you get a result. Unfortunately the cost of parts and the time taken in labour, even if you attempt the work yourself, it would not be economic considering the age of the appliance. I'd take comfort in the fact that it has provided 15 years of use, but now is the time to write it off and get a brand new machine. As technology has moved on in last 15 years, you will get better performance for much less than your Neff cost originally. I'd suggest you look at Bosch machines as they are made in the same factory as Neff and would be an excellent replacement.
Rupert, December 2019