We hear allot about bad caps. Well of the 23 various problems that I have found in the last year or so, 5 have been bad caps. An equal number had some mechanical problem causing it to not  work correctly. If we include dirty contacts that category jumps to 8. It would actually be higher because several pieces of gear have had dirty switches and pots that DeOxit fixed. I don't count those as repairs, that's just maintenance. Here when I report a dirty contact it is card edge or wire to pin type of semi permanent contact that has become open. Out of 7 power supply problems only one involved bad silicon. Out of all repairs 7/23 or about 1/3 involved bad active components. Mechanical\Dirty\Caps\Fuses are what I consider easy fixes, they account for well over half of the repairs. (16/24)

Don't just turn it on when you get it. It probably has been turned on, so you are most likely not causing a serious problem (but then someone else did, and you could be making it worse!), so my attitude is to crack it open first. I usually do this even on gear that is promised to work. I want to see if it is reasonably clean inside and has no serious mechanical or obvious electrical problems. I look for dirt, water damage (can happen in a warehouse or hamfest) , burned parts, signs of heat or smoke, loose parts, missing modules, missing screws, loose wires, and signs of "un authorized access" -  that is someone who didn't know what they were doing that did something.  Obviously any serious problems of that nature should be remedied before powering up

If it's an older vintage type of tube gear I will usually bring it up on a variac. Old electrolytics that are still servicable can leak alot when first powered up after a long off period. Bringing up the AC slowly keeps the surge currents down and adds an extra measure of protection to the old circuits. If you can find a power supply test point then you can bring the line up to about half way, the filaments should be on and the supply creeping towards the correct value. Bring the line gently up to about 80% and it should just about be working, or smoking! You can look for tubes that aren't glowing or are flashing odd colors such as purple.

After you have decided that you can power it up safely you then have to decide if it is working properly. That can be difficult, especially on the more complicated gear. My working gear is in two categories: 

1) Good enough to use. May have some problems and or hasn't been completely checked out.

2)  Works to specs, has had the checkout procedure applied to it, and\or has been used enough to be confidant of it's condition.

Most of my gear is in the first category, good enough to use, but might have a flaky feature or two, or maybe I haven't looked at every feature carefully. If you don't have a manual then any but the most simple gear is difficult to check out completely.