Did you try manually activating the "S Relay" as Fifty suggested? If you don't know how to do that, ask. Use a wooden or plastic chopstick and make sure the power is on -- be careful. If you see activity, it could be a bad "S Relay" coil. Unplug the AC cord and test that coil using a 9-volt battery across its 2 terminals: if it clicks or moves the switch plate, it's OK. While power is off, check for continuity between the credit button switch and the "S Relay."

Wait a second.

I just took a closer look at your photos. Those 2 (white?) disconnected wires you show dangling inside the coin door serve power to the coin lockout coil, but that's not all they do. It's true you don't need the lockout coil "energized" to start the game, BUT... according to the schematic, these wires use the lockout coil's winding to complete the start circuit. So...

Strip and twist the 2 white wires together with a wire nut, and you should get a start sequence. If not, at least it will get you to the next diagnostic step.

Those two hanging white wires were factory soldered together to one terminal of the coin lockout coil. Their color is not specific on the schematic. This should not cause a short. I checked this with all 4 of my Gottlieb-era models. Also, whenever working with scavenged or hacked pins, always have proper fuses handy.

Photo from a fully working Surf Champ inside coin door provides visual evidence. The 2 white wires were removed from one terminal of the coin lockout coil and tied together. The black (common) wire was removed from the coil's other terminal and left alone. (Joining the black & white wires WOULD cause a short in the 15A fuse). Note the slam N/C switch far left is wired per factory and left untouched (as yours seems to be also). Again, there may be other issues, but it's unlikely you will get a start sequence without doing this.

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Anti-cheat is the vertically mounted switch at bottom left of my photo (post # 17) mounted on coin door. Normally closed (N/C). Begin by checking it's solder tabs for continuity, or join them together. Do the same with the N/C "bounce switch" in that same circuit -- I believe it's located on the bottom panel inside the cabinet. Then refer to the schematic outline in post #4 and "inspect and diagnose this circuit with alligator clip jumper wires."