I am going to presume that it was working and now its not ? or did you procure the game in this state ?
Most electronic games, Pinball, Slots, etc have some kind of battery on board. Older systems had a type of logic with a built in battery, when the battery died the chip was basically toast.
I think these valley dart boards are newer than that.
I would start by looking for a battery on the circuit board. If your lucky this might be a quarter sized lithium cell, etc.
Next I would examine the board for acid damage. A leaky battery can do a lot of damage.