With credits on the game, pressing the start button does nothing, yet pushing in the start (S) relay by hand starts a game normally.

Start button does nothing but the start relay works by hand: dirty inertia switch

Cause: Power for the start circuit passes through two inertia (anti-slam) switches before it reaches the start button stack on the door. One of those stacks was loose and dirty, so the start relay never got power.

Checks

• Follow the start relay circuit back from the relay using the schematic: credit unit zero-position contacts, coin door plug, start button and the inertia switches in series with it.
• Look for loose or dirty contacts on the inertia switch stacks and on the credit unit switch that shows credits are present.

Fix

• Clean, tighten and adjust the inertia switch stacks so they close firmly, then test the start button again.

Unplug the game before cleaning or adjusting switches; parts of an EM game's wiring carry line voltage.

Systems

• Electro-mechanical

Games

• World Fair

Related tips

• Credits register but the start button does nothing
• Ball count runs to 10 and the game resets endlessly: dirty ball count stepper
• Start button adds players 1 to 3 but never the 4th: adjust the coin unit end switch
• Game won't start though credits and reels reset: bad joint on the latch coil
• Game Over relay trips again right after start: dirty Lock relay switch
• Game resets but the outhole relay never fires: feed wire hanging by a strand
• Game starts but flippers are dead and nothing scores: dirty relay switches
• Push relays in by hand gently and straight

Source: Pinball Repair help group!! (Facebook group)