If I'm afraid to turn something on, it's because I've failed to address the risk factors.
There is no perfectly safe thing. But one needn't be a damned fool about it. One can only be as safe as is reasonable.
Mind, not even "as safe as possible", because quite safe operations may be
possible, but they will be extraordinarily prohibitive, in time, money and flexibility, to implement.
OSHA for example is pragmatic when it comes to workplace safety. They do not prohibit people from, say, reaching inside live breaker boxes with their hands. Not unconditionally so. But you'd better have a damned good reason to do it in the first place -- having no better way to address the problem with tools (e.g., not enough dexterity with a probe-on-a-stick), and taking every other precaution you can (thick rubber gloves TESTED RECENTLY are a must!).
While testing a little electronic circuit is hardly a life-or-death situation, the exact same principles can be applied on any scale, for any cost (be it a human life, a multimillion dollar facility, or a ten dollar charger that you don't want to have to get off your ass and buy a new one of just yet).
So, identify those risks.
For equipment repair, what are you afraid of? Capacitors and transistors exploding? Resistors catching fire? Holes being burned in boards? Burning out fuse after fuse, not learning any new information in the process?
Identify possible causes. Create hypotheses
AND THEN TEST THEM!Example: a power supply is turning on and off, strobing, even when lightly loaded. This is most commonly caused by an intended mechanism: the controller is self-powered, and when it isn't receiving power, it times out, shuts down for a while, then turns on again and so on. You might test if this has failed, by tacking pigtails onto the circuit, and powering it with an isolated supply. If it's still pulsing, you've at least ruled one thing out, but if not, you now have much more information available to test: is it switching? Is it generating output? Is it generating auxiliary power after all? And from here you can narrow down the possibilities much more rapidly.
Say you get a piece of equipment and it's got a blown fuse. Well, it's a good bet that something blew that fuse. So, don't just go replacing the fuse, then plugging it back in to test. That's a low-information result: a likely waste of fuses. Follow the AC power into the circuit, and check for shorted diodes, capacitors, transistors and so on. Only if you have not identified a likely problem, go ahead and plug it in. You've at least then gathered a few bits of data, rather than ~1/2 a bit. If it fails again, you know it's probably not the things you just checked, so get more creative, check more unlikely targets. Instead of ohming it out for shorts or opens, use diode test and see if the semiconductors look reasonable. Apply a stimulus or external power and see what happens. There are many circuits you can test in blocks, this way -- something akin to attaching life support machines to a patient undergoing major surgery.
Even at the instant of turn-on, you can minimize risk. Use a current-limited supply; increase the supply voltage gradually; supply aux power to circuits that can't operate so low; etc. If the circuit has large capacitors in it, consider disconnecting them (so that, if one device fails shorted, it doesn't dump the entire charge through the circuit, taking everything else down with it!), or isolating them with current-limiting resistors.
Some of this does require extra attention (who wants to pull out capacitors or cut traces?), or extra equipment. I personally have created several current-limiting devices for use on my bench -- I have a 24V battery circuit available here, and they are an excellent way to deal with the hundreds of amperes short-circuit capability!
This was rather lengthy for a beginner's thread, but I hope that at least bits and pieces of it shall prove useful to those wondering.
Cheers,
Tim