Cord Rewinder or Circuit Board
Chances are most likely it's the cord rewinder that's broken. What happens with Miele cord rewinders typically is the 2 sides of the cord rewinder will separate, just a tiny bit, enough that both sides of the electrical contacts in the middle will no longer make contact and send power to the rest of the vacuum components. The easiest way to diagnose a broken cord rewinder is to take out only a little bit of cord, and plug it into a extension cord. Then turn the vacuum on. Pull out a small section of the cord from the rewinder - if it starts and stops when you do this, it's the cord rewinder that's faulty and causing your issue.
However, it could also be the circuit board at fault. Ever since the Vortex Motor was introduced in 2004, the circuit board that interacts with the wiring harness that connects to the motor has been a issue, and it's VERY COMMON to see the circuit boards go bad within 10 years of ownership. Furthermore, the really damning part is, with the Vortex Motor there is NO WAY to bypass the circuit board if it fails! The motor is designed in such a way that you MUST use the wiring harness & 4 pin connector & receptacle. Due to the complex way the Miele vacuums are wired, it is not possible to bypass that wiring harness attached to the circuit board that sends power to the motor if the board was NLA, even if you replaced the motor with a ordinary 2 wire Domel central vac motor. If your circuit board dies and it's NLA, you are literally up the creek without a paddle! For this reason, plus the fact that the German made double stage motors and Ametek double stage motors Miele used prior to 2004 produce as much waterlift/CFM and were far better made and more durable, I no longer recommend anyone buy a Miele made after 2004. It's just not worth it - especially when you can easily find parts and parts machines for the older models.
Take it to your authorized Miele dealer and have them diagnose the issue, assuming it's under warranty. If it's the circuit board and it's under warranty, repair it. If it's NOT under warranty, junk the canister and sell the hose, wand, powerhead and parts. Replace it with a older Miele - preferably one from the S300, S400 and S500 series. There are 2 Miele models in particular that did NOT have a circuit board in them at all, the S301i and S401i, that I would try to find and buy. Otherwise, buy another brand.
If it is the cord rewinder that's faulty and causing the issue, DO NOT REPLACE THE CORD REWINDER! Tell the authorized Miele dealer to put the vacuum back together, pay whatever their fee is, and take it to their competition. The cord rewinder can be repaired by putting a metal ring and pin on the plastic spindle on the cord rewinder. That will cause the 2 halves to make contact, conduct electricity and work properly. It will also PERMANENTLY repair the cord rewinder - you will have no future problem after that. If desired, it is also possible to wire a upright vacuum cord to the electrical wiring on the cord rewinder and bypass it entirely. Sure you won't be able to neatly store the cord inside the canister, but again it will NEVER break again.
Rob