Pinball is generally robust... and designed for technicians who make mistakes when they are servicing a machine a 1:30 AM (because the bar is open until 3:00 AM...), and the cigarette smoke is thick enough to cut with a knife, and the music is so loud that you cannot hear yourself think. And drunken people are leaning into your work giving you advice.
That having been said, I'd put the board in the game, screw down all the screws firmly. Do not plug in anything, then plug in J17 (top of board a little to the left). This is logic power. Power up to see if the LED's (blanking, diagnostic) are doing what they need to.
Then I'd probably plug everything in and see if any coils hold in on power up, if any fuses blow...
It would probably be safer to plug in the display stuff, and the diagnostics switches and the sound stuff, see if the sound board is working by going through the diagnostic menus. Then plug in the switches, and test them through the menus, then the coils last.
But honestly, if the game does a power up diagnostic LED test, the other stuff is trivial to fix (as far as these repairs go!), and I'd probably just fix whatever is wrong after I'd fully connected the board.