I've watched videos of Ronnie Lyons in South Carolina fixing old pinball and arcade games. The latest video has a pinball machine that is 65 years old. It was from the time period that they were still using wooden side rails, and a cigarette holder came as standard equipment.
There are some repair techniques that are common to all of these machines. Cleaning all electrical contacts and plugs applies to all of them. Often, that fixes the majority of the issues right there. From there, one would want to check all the voltages and see that the correct size fuses are used. If they are too small, they will likely just blow, and if they are too large, that can lead to catastrophic failure in the event of a problem. If there are large capacitors, and they are original, you most likely want to change those. Sometimes, you want to go even larger with high-value power filtering capacitors, such as when the cabinet and playfield lights flicker when you do something on the playfield. With solid-state pinball machines and arcade games, you may need to rebuild the power boards. It is best with most of these machines to work your way in from the power cord.
Rebuilding the power boards isn't too hard. Just test all the semiconductors and change what is broken, change the capacitors on the board, reflow the sockets, and replace the connectors if necessary. Sometimes you run into parts availability problems. For a number of the power boards, there is room for larger rectifiers on the other side. If you can't find the 3-5 amp rectifiers, you may have to use 30 amp replacements, so you'd have to mount those on the other side of the board, and you likely won't need to add any heat sinks. In some cases, you will have regulators putting out too much power. In some cases, that is a design flaw or from using a different part than what was called for. Sometimes, you can jumper over the nearby resistor to reduce the voltage. There is also a pot to adjust the high voltage output line. While that should be around 190 volts for the plasma displays, you may want to use a little less to help save the displays (they don't make them anymore). On the power feeding the MPU board, you don't want that to be much over 5 volts. If it is 5.2 volts, that is one thing, since there is voltage loss in the wiring, but it can be a problem if it is putting out 5.6 volts or more. If that is too high, it can damage the MPU board or other boards such as the sound board.
There are 2 categories of pinball machines, electromagnetic and sold-state. The EM machines use motors and relays for everything. Most of the problems on those are related to bad connections or misadjusted switches/relays, though you will find broken parts on occasion. You don't want to adjust every switch, just the ones that are obviously messed up and those tested as not working. There are parts that routinely wear out such as the plunger tip, the rubber rings, the flipper shoes, etc. There is a scoring motor on the EM machines. On rare occasions, the cam will break where it attaches to the motor. That will be a problem since you can't get the cam anymore. If you run into that, you will need to hack a solution. There are stepping units that should be disassembled, cleaned, and lubricated. The same goes with the score reels.
You may run into PCB trouble on solid-state machines. If you have major issues, you should check the playfield for problems before reinstalling and attempting to use any boards that you repair. For instance, if a solenoid and a switch are touching or miswired, that can send solenoid voltage up digital lines and possibly damage the MCU board. That is why most who repair the boards don't like to do so without having the entire machine. (Similar goes for automatic transmission repair. They want your vehicle so they can clean any debris from the transmission cooler under the radiator so it won't damage the new or rebuilt transmission.)
You have to be aware that some problems manifest in multiple places. For instance, solenoids and transistors often fail together. Either the transistor shorted first and caused the coil to lock on and short from overheating, or a shorted coil damaged the transistor driving it. Sometimes, that is caused by a misadjusted switch. There are 2 coils inside the flipper solenoids. A normally closed switch shorts the finer coil to give more power so the flipper will move rapidly. Once the flipper is fully extended, the switch is supposed to open and reduce the power used as the flipper is held in place. If a flipper is weak, it could be that the end-of-stroke switch is misadjusted or dirty, or in some cases, particularly with the EM machines, the switches behind the flipper buttons are dirty/worn.
It is a good idea to change all the bulbs at once. You really don't want to tear back into the machine anytime soon when the others blow. If they use #44 bulbs, you may do better to replace them all with #47 bulbs. They are slightly dimmer, operate cooler, and use less power. That helps reduce melting parts on the playfield, and with solid-state machines, that can help the driver transistors last longer. If there are still bulbs that don't work, the next place to check would be the sockets themselves. You can often wiggle the bulb or rotate the socket where it is riveted if that is the case. If you still have bulbs that are out, then check the switches that are driving them (on an EM machine), or check the light driver board on a solid-state machine. The first thing to do if you suspect the light board is to inspect the plugs. Replace the connectors if you need to. Then make sure the connectors have good solder connections. So reheat all the solder joints to the connectors. Then test all the transistors, particularly the ones that schematics suggest are involved, replacing them as needed. Now, if a whole group of lights is involved, you sometimes need to change the chips feeding the transistors.
On plasma displays. If they are not working or have weird issues, there are several things to try. Inspect the "glass" part. If there is a hole, signs of a leak, or burned digits, there is no way to fix the display. Just keep the board for parts. If there are no obvious problems, then check the components. Check the transistors and the values of the resistors. Once you change those driving the digits involved, it may be the IC if it still doesn't work. Of course, if none of the displays work, it could be a problem on the MPU board, or rarely, all the displays are indeed bad. If you cannot fix the displays, there are LED retrofit kits. Depending on the machine and the upgrade kit, you may be able to change just the affected displays or maybe not. If you must change them all, you can remove the fuse to the 190v power rail, since you won't need it. If you upgrade the displays to LED ones, certainly keep the plasma displays, particularly the working ones, since you may need them for another machine.
On arcade monitors, if they don't come up, you should rebuild the deflection and high voltage boards. Clean and reflow the connectors as with everything else. Change all the capacitors if they don't appear to have been changed. Check the fuses and semiconductors, replace what's needed, and install the correct fuse values. For some machines, if you change the capacitors, then you should also change the flyback transformer if the original is still installed. They may have cracks or other issues, and restoring the original voltages may damage them. So on the machines known to have this issue, replace the flyback when you rebuild it. If you find that your display changes size after the monitor warms up, that is likely the high voltage rectifier. If you have unusual color shifts, that could be short in the CRT. In that case, change the CRT if you can find one. There are also some hacks that some try such as building a power supply just for the filament to mitigate the short. But then, things are not original.
For the MPU board (in either arcade or pinball machines), besides cleaning and reflowing the connectors, you should lift all the socketed chips out, clean them, then reseat them. If the machine's self-test shows that the RAM is bad, that is not necessarily the problem. It could be, or it could be the nearby buffer chip. A logic probe is mostly what you'd need for troubleshooting. Another place to check is the CPU watchdog circuit. Sometimes a nearby buffer may be bad, and occasionally, a sound chip if one is located near the CPU.
With sound boards, you should do the usual work such as cleaning and reflowing connectors and cleaning and resocketing any socketed chips. If you're missing certain sounds, you may want to try swapping any POKEY chips. Sometimes a logic gate or an opamp may be bad. Just follow the schematics to where the missing sounds are produced.