I've pulled apart one of my PS1's because I couldn't figure out how you're making this so difficult.
The led you've left on the switch board isn't connected to anything, so I assume this isn't the led you're talking about lighting up.
The contacts switch from one side to the other, not front to back....
In other words, if you have the board sitting in front of you, as it would sit in the PS1, the left contacts are the "input" and the right contacts are the "output"
Meaning, the way you have it wired above, you're simply shorting out the power supply, and the wire points need to be rotated 90 degrees...