MMMM- just a thought.. but if AX relay is energising but not holding in yet mechanically it is sound then the problem MUST be elsewhere.

There is an "R" relay - this should pull in and de energise the "game over" relay... if this isnt doing its job then the machine will automatically go into Game over mode and not start.

Fire up the game keeping an eye on the Game Over relay - the contacts should open - if this relay stack doesnt move then you need to look at R relay which triggers it