Steffen, you're not giving us much to go on. You say the motor doesn't run; does it do anything else? Is there any kind of indicator light that comes on? There's a red indicator light beneath the warning sign to the top left that can indicate an overheat condition or a damaged overheat switch. If that light is on, I suggest you read up on the vacuum cleaner disassembly guide here.
[guide|139313|Miele S828 Vacuum cleaner Disassembly - iFixit Repair Guide]
Otherwise you will have to do some basic troubleshooting. Can you use a voltmeter and an ohmmeter? If so, you'll need to disassemble the vacuum and test the power switch then check to see if the motor is getting power.