As AJ said, most components are hard to test on-board.
At most times, some components appear dodgy until i left 1 leg off the board and re-measure to find it's OK.
Resistors & Diodes are typically OK on-board, however a diode across a coil/relay will appear "short circuit" as you're really measuring the coil.
Capacitors can be measured ON-board with an "ESR meter" (this great kit is from Jaycar & Altronics).
Once again this isn't always perfect, and lifting 1 leg off board will give more accuracy.
Some people say to measure a cap with your multimeter set to 'volts', and if you get a brief 'pulse' of voltage reading, than the cap is holding it's charge.
However, a 1,000uF cap that is leaky and acting as a 200uF cap, will still hold a charge.
You can't go past buying yourself a Capacitor meter ($60ish), and/or an ESR meter kit ($60-80ish).
Check the tops of capacitors, that small silver flat top should be FLAT, not bulging or popped open (usually has brown gunk pushing out of it - these are dried & fried caps, obviously need replacing.
Caps also fart out underneath,look for brown gunk around their mounting legs too.
Transistors are hard to measure on board too, even lifting leg(s) off board doesn't prove they're OK, as some Transistors measure OK to normal multimeter tests, but they breakdown under heavy load when back in operation.
You can 'force' transistors to switch ON while on board, usually by injecting some voltage onto its 'base' pin.
You really need to know what you're doing a this level, you need to remove any driver chip from it's socket so you don't blow it up etc etc....
FORCING components ON/OFF is good if you REALLY know how to read schematics and understand what 'else' will be affected.....BEWARE !!
I usally buy replacments trannies for anything i measure as 'suspect', if i replace the tranny, and the fault is still there, i know the tranny i pulled out is probably OK too, and goes back in my "used tranny" draw.
IF you wanted to get a little more techy, you could buy a transistor checker kit, as long as you know which leg is which (base,collector,emitter) then it'll be ok, but once again that tranny might breakdown under higher voltage/current conditions.
You could also setup a battery, switch and an LED or relay on a small board, and plug in various trannies and see if the relay turns on, proving the tranny works, what a pain.
You can spend far too much time measuring and analysing parts in your pin, when you could simply replace the suspect parts in 1 hour, and have a working pin, and "know" which part was the problem that you've changed.
MM.