Ah yes, unplug it, and plug it back in again whilst rotating the chuck to and fro. It’ll enter diagnostic mode, where you can use the switch to enter the code to reset to factory settings. Sounds like it’s gone into temporary safety mode after detecting a possibly dangerous situation, so this should cure it.
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It’s a motor connected to the mains. If there’s a blue flash and smoke, it’s buggered! Burned out, failed, dead, an ex-Dremmel if you will. You might be able to take it apart and re-wind the motor or something but that’d be a right old faff.