Troubleshooting a circular saw that quit working
Here's a first-stab at a troubleshooting guide:

With the unit unplugged and/or the battery removed:


Visually inspect the tool...


Is anything potentially jamming a mechanism?
Are the air vents clogged?
Has the unit been exposed to too much dust, ash, water and/or fine sawdust?
Is the case discolored or cracked at any spot?  
On the power cord, is the insulation cracked at any point or is one or more strain-reliefs damaged or missing (especially where the cord enters the tool)?
Are the plug contacts reasonably straight and untarnished?
Is a fuse or reset button present?  Is it blown or popped out?
Was the tool used until it might have become too hot?  Many tools have a safety, over-temperature shutoff; wait an hour for it to reset.
Is the safety switch/lock, if present, installed and/or on?
If the unit came with a grounded plug, be sure that it's undamaged and that the power plug really is a properly wired grounded outlet.  Use one of those circuit checkers you can get for $2.
Has an oily, greasy, or varnishy fluid dripped or oozed out of any part of of the unit?  Grease could indicate bearing failure.  Other oozings would point to catastrophic motor damage, or sometimes electronics failure or starting capacitor failure.

Does the tool rotate/reciprocate relatively normally when moved by hand?
Does the the power switch feel normal?  Usually a busted switch will feel "off" (Pardon the pun.)
If you are comfortable with an ohmmeter, you can use it to do basic checks on the cord and switch.  Note that it is possible for a circuit to look okay with the meter and still be bad under load -- or for control electronics to be bad.  



With the unit powered:


Does the motor hum or smoke when turned on? (Of course, Immediately switch it back off if it does this.)
Does a circuit breaker trip?
Do you feel an electric shock?
Does the motor arc excessively?
Any unusual noises? Humming, or squealing?




If the visual inspection is failed, it should be obvious what to do.


For a damaged cord, replace it. Do not attempt to repair it.
If the case is plastic and is discolored anywhere, it has likely degraded to the point that the tool is either unsafe or it's just not worth repairing.  Some uniform case discoloration due to age and UV exposure can be okay -- as long as the case is not also cracked or brittle.


If the switch feels funny and/or nothing happens when it is turned on, then it could well be a busted switch -- which is pretty common.  You can sometimes get replacement switches at a reasonable price.

If the motor arcs excessively (a little visible arcing is normal), the brushes may need replacing.  Do not run the tool if you suspect brushes, you can permanently damage the motor.

If the motor hums or smokes, it's typically one of these problems:


Something is mechanically jammed.
Bad switch.
Bad power cord.
Bad control electronics, if any.
Bad, broken, or burnt internal wiring.
Bad brushes or damaged commutator plates.
Bad starting capacitor (if used).
Bad starting coil.
Improper outlet voltage and/or grounding.