This is your outhole switch actuator arm (red circle). When in this down position, your leaf switch is closed, or should be (red square). Take this arm and adjust it so that it goes into the slot next to it, up through the playfield. The leaf switch should open. Manually actuate the arm and make sure that it closes the leaf switch.

To test, start a game, score some points, then use a pencil and with the eraser side, press and hold the leaf switch down. The bonus should count down, then you should hear the ball eject solenoid. Clean the contacts with a business card, crisp dollar bill, or 600 grit sandpaper.
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As far as the disconnected wires, they likely should be attached to a switch and in this particular picture, it looks like a switch on the bonus unit. You'll need to find where it goes and reconnect it. Same with other broken wires. Find the switch that it goes to and reconnect it.