After troubleshooting the machine is finally running again. I started with the electronics and concluded that all drives was still working. Eventually I understood that the motor was causing the problems, it was completely stuck. I did not notice this at first because of a mechanism that let you turn the ballscrew from the outside.
I removed the motor and took it apart only to find that my servomotors had breaks in them! I had no idea about this so I never plugged them in. I can’t even find them in the drawings. I knew that some servo motors have breaks in them but I thought mine was without.
This is most certainly the reason my motors got so hot before, I didn’t thought it would be possible to run the machine with the breaks engaged.
I'm glad it’s working again and I actually feel quite sorry for my milling machine this time.