Yep agree with Fredmythson and to add if you don't have a schematic, below is the startup sequence for Target Alpha taken off Mr. Pinball site. It looks like your at step 6 in the sequence, but still could be an issue earlier in sequence with score reel switches really not indicating True "0" state for example.
As a quick start I'd manually put all score reels at say 55,550 and see if they are all going back to 0 at start of game, but maybe you've done that. If they are all going to 0 then I'd visually inspect all the switch stacks and motor switches starting at step 6 in the startup sequence when you hit the start button to see what they're doing and maybe you'll spot where the sequence is stoping. Also make sure no lose wires, hacked stacks or blades, or something obvious you can spot. Then with power turned off the machine, I'd manually activate them to make sure they are opening, closing, as they should. A tightening of switch stacks and then cleaning while your looking at them with power off is a good thing to do as well.
Good luck, great game in my opinion
Mr. Pinball Tip:
The following information is taken from the November 1976 Gottlieb Target Alpha manual. This may be helpful when debugging a startup problem with this or other Gottlieb 4-player games from the same period.
1. Inserting a coin or pushing the replay button actuates 'S' relay (Start relay).
2. This relay will lock-in through its own switch and a motor 2B switch.
3. 'S' relay starts the motor running.
4. 'AX' relay actuates and the 'coin' unit subtracts through switches on 'AX' and 'S' relays and switches on motor 4C and motor 1A. 'Q' relays de-energizes when 'AX' relay operates.
5. When 'AX' relay actuates, the reset relays 'Z1' and 'Z2' are energized in sequence by rivets on the 'Player' unit, through switches on 'AX' relay.
5a. Motor 1A steps the 'Player' unit, through switches on 'AX' relay and 'P5B', to the 20th position energizing 'Z1'.
5b. When 'Z1' is energized the 1st and 2nd player score units reset to zero through switches on motor 1A, motor 4A and 'Z1'. When all score units of the 1st and 2nd player are at zero the player unit steps to the 21st position through a normally closed switch on 'Z2' and normally closed switches on all score units of the 1st two players, actuating 'Z2' relay. The 3rd and 4th player score units now reset through switches on motor 1A, motor 4A, and 'Z2'. The player unit continues to its zero position through the closed switches on 'Z1', 'Z2', 'P5B' and motor 1A until 'P5B' opens.
6. When 'P5A' on the player unit closes, 'AX' and 'BX' relays reset through motor 4C and switches on 'DX', and 'R' relays. The reset cycle is now complete.
7. Inserting additional coins or pushing the replay button will step the 'coin' unit through switches on 'DX' and 'S' relays and a switch on motor 4C. The replay button circuit opens when 'coin' unit is on 4th position.
8. Place the ball in the out hole. The ball return switch closes and completes the circuit to 'O' relay through the normally closed switches of 'DX', 15th position 'Bonus' unit, motor 1C, motor 2B, 'Q', 'AX', and 'S' relays. 'O' relay locks-in. Through switches on motor 4C, 'BX', and 'O' the ball return coil actuates kicking the ball onto the runway.
9. The remaining balls that enter the outhole are kicked across the trough switch which pulls in 'P' relay. 'P' relay runs the motor. Switches on 'E', 'DX', motor 2C, 'P', 'BX', and motor 1A advances the 'Player' unit the required number of steps determined by the 'Player' unit switches and the 'Coin' unit.
10. The 3-5 ball adjustment changes the number of balls played per game. The third or fifth ball leaving the playfield will trip the 'last ball' relay 'BX' through switches on 'E', 'DX', rivets on the player unit disc, and 'O'