There is a single fuse (F1) in the vertical twist-cap style holder on the power brick. But if that is bad there'll be no power anywhere - no marquee light, no monitor glow.
Next is the interlock system - the white plungers that are installed at various points depending on which game. Asteroids has one for the back door and one for the coin door. They are pushed inward to their momentary position when the doors are closed. If either one is faulty or not in the proper position then the door may not be activating the switch. Note that for the coin door it is the coin counter (black odometer thingy) that pushes against the interlock. If it's missing then no plunge of the switch = no power. Most have a service position where you can pull the plunger outward. The interlock circuit plugs in to the power brick with a six position connector, in line with F1. If it is not plugged in then power gets no further.
Next is the voltage selector plug, also there on the brick. It is a nine position connector with various short loops of wire that configures the brick for the local AC voltage. For 120vac the brick should be using the plug with the yellow wire. If unplugged, power gets no further.
If all of the above is working and the power switch is turned on, power will make it to the main transformer on the brick. You will probably be able to hear and/or feel it humming. If it is working and connected, the marquee light should also turn on.
After that is the row of visible fuses on the power brick which is what the owner has probably checked.
After that, various voltages go to various places throughout the game. The monitor may have neck glow and/or the spot killer LED may be on. That LED indicates the monitor is not getting a signal from the game PCB (it's not a power indicator, but then again it won't light up unless there is power).
The audio/regulator board is next, taking some of the voltages from the brick and adjusting them for the game PCB. There are labeled test points on the board, so if you have a meter you can test for their presence. Note that you may have some voltages but not others, depending on whether components on the AR have failed.
Last is to check the main PCB. It has a LED that will indicate the presence of 5v, but the LED may have failed. Use the nearby test points to check for 5v.
In any case, if you are thinking of buying it, don't let missing power dissuade you. It can be tracked down and restored.