Blown computers and tablets due to blackouts and brownouts
First: Under-current shouldn't actually damage properly designed equipment -- most power regulators have under-voltage lock-out features. Is it possible that inductive transients have over-volted the equipment as part of the off- or recovery events?

Second: You will have to open up the equipment and start trouble-shooting. This may mean going into enclosed power supplies; if you are not experienced with mains electrical work, this would be dangerous! Once you troubleshoot the equipment, you should be able to trace the problem to some particular component -- there should be voltage, but isn't. That shows that such component is broken, and with luck you'll be able to see it physically (but not all breakage leaves physical marks -- some breakage just has to be measured.)

Also: Make sure it's not something simple like a blow fuse or circuit breaker :-)