Hey there, are these 4 points pretty distant and "sporadic" from each other or does it sound like a evenly-spaced quick "TOCK TOCK TOCK TOCK"?
This will let us know if it is a 1-point switch shorting with the vibration of the machine or a malfunctioning 5 point circuit.
Additionally, if you give the score motor a spin in the cabinet (with the machine on - just give it a little push on one of the pegs in the proper direction, it will carry itself the rest of the way until it finds the home position), does it also award these points? I'm thinking it is a misadjusted switch, but a rare occurrence COULD be that there as a misadjusted switch somewhere in the 5 point circuit that is triggering, when the score motor is running for the startup sequence. A machine should not do anything when you give the motor a spin (besides spin itself back to the home position - it will be very quiet), except in rare cases where it's in the game's design.