I'm assuming by resetting you mean that when you push the start button the score motor and all the score reels continue to run without stopping. On EMs all units need to reset to zero before it will start a game. Sounds like one or more is not. Score motor should rotate three revolutions which gives all score reels and player, ball in play units time to get to zero. If not the score motor will continue trying. Most common problem is one of the score reels doesn't reset to zero

Everything needs to go back to the home or zero position not just the score reels. So if the drop targets are still going up and down and the next player keeps going sounds like both of them are not in the home position. Move the player up to home and check that the switch is actuating and with a meter check the resistance to see if its near zero. Cleaning contacts without checking with a meter doesn't ensure you that they have zero resistance. Same with the drop targets or anything else that keeps running. Sounds like all score reels reset to zero as they should so its not them. Check ball in play as well.