Yes, this very well could be a problem with the cord reel, especially if it happened all of a sudden. There's a few ways that you can diagnosis this problem yourself. First make sure the cord is all the way reeled into the vacuum. Next find an outlet that's close, and only pull out enough cord as you have to, to be able to reach the wall outlet. After you've plugged the machine into the wall, use one hand to slowly pull more cord out of the vacuum, and use the other hand to continuously turn on and off the vacuum pushing the foot pedal that controls the main switch. Slowly pull the cord out, and turn the vacuum on and off, on and off, on and off.
At any point while you were doing this did the vacuum come on, even for a very short time? Did it even make a noise like it was trying to start? If you heard a noise, or the vacuum even came on for a time, then this definitely indicates that you have a bad cord reel.
If it didn't make a noise or come on, you still may have a cord reel problem, but you'll need to take the machine apart to further diagnosis it at this point. A simple continuity electrical tester will be needed to test the cord reel.
Here's a very detailed repair instruction that I left for a similar model Miele on Fixya already. The model that you posted the repair under is a Miele Red Star which is an S314i, the model I repaired the cord on was actually a S514. The cord repair on both of these models is identical however, except your Red Star actually has two screws that need to be removed from the variable speed control box, the S514 only has one. Otherwise, it's almost completely the same repair. If you need to purchase a cord reel for your Miele, here's a direct link to the Miele S300 series cord reel that goes with your Red Star:http://www.govacuum.com/miele-cord-reel-s300-series-06777540.html
Even better, if you purchase the cord reel from GoVacuum, you have 60 days after the purchase that you may return the cord reel to us if that wasn't the problem (we do test all the returns to make sure that they weren't damaged when being installed), and as long as the cord reel is returned undamaged, we give you a full refund, we don't believe in restocking or shipping fees. Better yet, we even include a return label with every order that you may use for free to avoid return shipping charges.
If you find that the cord reel is not the problem, that can only leave one of three things; the switch, the motor, or the pc control board that's on your motor. In 10 years of fixing Miele vacuums however, I can safely bet that it's your cord reel.
Anyways, here's the link to step by step instructions on how you can remove the cord to test it, as well as replacing it. If you have any questions, please feel free to use the Clarification or comment form here on Fixya, or contact us by phone. If this was helpful to you, please be so kind and rate my repair as helpful by clicking the thumbs up icons at the top of the page. Thanks so much!
How to Test & Change a Miele Cord Reel: