No coils work at all.

No coils fire: check the 28 V solenoid supply

Cause: Blown solenoid fuse F2, or a shorted or partly failed 6BR2 solenoid bridge rectifier in the backbox.

Checks

• With F2 fitted and the game on, put the black meter lead on power supply connector 3J4 pin 1 and the red lead on 3J3 pins 6-9: expect 28 to 47 V DC (it reads higher unloaded).
• No voltage: check F2. If F2 blows at every power-on, the bridge has probably shorted.
• Low voltage: the bridge rectifier has probably partly failed.

Fix

• Replace F2 with the correct rating, or replace the 6BR2 bridge rectifier.

Line voltage is present in the cabinet and backbox with the game plugged in; unplug before working on wiring.

Systems

• Williams System 3
• Williams System 4
• Williams System 6 / 6A
• Williams System 7

Related tips

• No solenoid voltage
• What the power supply board takes in and puts out
• Test the power supply with its outputs unplugged
• Swapping power supply boards between generations
• No +5 V on a System 3-6 power supply
• No +5 V on a System 7 power supply
• Early Black Knights use the System 6 power supply
• High-voltage supply rebuild parts, System 3 to 11C

Source: Repairing Williams System 3 to System 7 Pinball 1977 to 1984, Part Three, Clay Harrell (pinrepair.com)