That coil is not needed for home use, but if you are not going to use it you'll need to adjust the switches on the lock relay as if it was activated.

Before doing more testing, I'd suggest straightening this mess up. The outer switches look like a make break and they are touch the 2nd switches in the stack which appear to be a normally open pair.

strat (resized).JPG

The outer switch (2 leafs farthest from the coil) should be adjusted so it is open. These two switch leafs should not touch the 2nd set of 2 switch leafs.

The other three switches should each be adjusted closed, but not touching the adjacent switch. For reference, here is a diagram of the switch in its off position. You've cut the wires to the coil, so now your going to adjust the switches as if the coil is activated. Instead of one normally closed switch and 3 normally open switches, you'll want one open switch and 3 closed.
stratlock (resized).JPG

The playfield should also be lit. Check your fuses and made sure you have good bulbs.

Looking at that relay I think it is possible that the switch that you have open might be closed because that huge lump of solder is touching the base of both switch leafs.

stratsolder (resized).JPG

Here is a video illustrating the 4 Player Williams reset sequence. It might help you to determine what's happening.

The top switch on the index cam of the score motor (the cam farthest from the actual motor) is the switch that pulses the 1 and 2 player score reel reset relay in the head of the game. Take a look at that top switch and make sure it is making contact as the high point on the cam pushes the switch stack up.

stratscoremotor (resized).JPG

A guess on the game over relay issue.. In post #37 I mentioned the blob of solder that may be closing the last switch on the lock relay. That last switch would lock on one of the game over relay coils. Have you tried to remove that blob?

The Coin Unit stepper inside the cabinet conrols the number of players. It has 4 positions. Pressing the plunger into the small coil should reset the stepper to a 1 player game. Pushing the plunger into the large coil will advance the stepper for additional players. You can tell how many players the game is set up by checking the backglass in the Can Play area.

When the 4th player position is reached on the Coin Unit stepper, a peg on the gear opens a switch. If this switch gets opened in a position before the 4th, I believe it can prevent additional players from being added. There is a great photo on pinrepair.com showing a coin unit stepper in the 4th player position with the switch open..here

http://www.pinrepair.com/em/wcoin1.jpg