Dremel doesn't power on: brushes?
My experience is that the brushes sometimes become stuck in their channels so that they no longer contact the commutator.


Remove the brushes (if the spring pops off, pull gently with tweezers). 
Clean the channel with a cotton swab. 
Put a single drop of lubricant on the brushes.
Reinsert, keeping the curve of the brush so it conforms to the curve of the armature.


That often fixes the issue until the brushes are worn down.