Try running it in Safe Mode (boot with Shift key pressed until the progress bar comes up - about 30 seconds). You will have 'Safe Mode' in red top left of screen if successful. Is the the iMac now stable? If so, your problem may the same as mine appears to be ie an over-heating GPU (graphics processor unit - video card). To test this, install smcFancontrol which allows you to speed up the CPU/GPU fan (it is shared by both) and see if the extra cooling stops the shutdowns. The other thing you could try is to disable Quartz Extreme which is OSX's graphics accelerator software. This is for when running in normal mode. My theory is that because QE is disabled in Safe Mode, the GPU does not work anything like as hard as when QE is running and so does not overheat so no shutdowns. I am about to try these on my iMac and will report back... MW
Armature; - Try operating the drill and twisting the chuck by hand (in the correct direction). If it starts then: Commutator ring: Is it shiny? If not take it out and clean carefully with some plumber's grade of wire wool. Make sure you clean it carefully afterwards to get rid of all the wire wool bits.
If that fails, What voltage do you get at the brushes when the trigger is pulled max?
Check the condition of the battery contacts in the base of the drill. They get worn/pitted/carbonised with use and whilst the poor connection is able to supply enough power to light the work LED (very, very little) as soon as you ask for enough juice to turn the motor, the resistance is too great and nothing happens. It is very similar to the effect in a car when the accessories, dash lights etc work but the engine won’t turn over - due to a poor battery connection. A new contact assembly is very cheap and easy to change (UK£10 or so).