If the large rotary switch moves up and down slightly, it's likely that the motor has detached itself because the rubber bushes have perished as shown in the first picture. Parts of the failed bushes may have fallen down into the control electrics and be visible if you turn the machine up side down. New parts can be ordered on ebay for about £15.

The aim is to insert new bushes into the motor's mounting flange as shown by the blue arrows in the second image.

Do not be tempted to use a simple metal washer to re-secure the motor in place, because any fault with the motor could put a live voltage onto the mixer's body and it is not earthed.