Krye:
Here's my experience:
There is a switch on the back which cuts off all power to the machine. Switching on that alone doesn't turn the machine on (at least not the Performa 575 I have). To turn it on completely (and therefore illuminating the indicator light) requires that the power button on the keyboard be pressed, which signals the logic board to do it's thing by activating the power supply. Without a logic board (or with a dead one), that's not possible, so no matter what you do, nothing's going to happen.
I will check out my Performa tomorrow to confirm all this.
Also make sure the edge connector inside (the thing the logic board plugs into) is undamaged and making good contact with the edge connector on the logic board. Mine went intermittent for awhile (the video would go blue or red, and occasionally go out altogether) until I slid the logic board in and out a few times, which apparently cleared some corrosion off those connector pins, because it's been working fine ever since.
As a last resort, you could try cleaning the logic board. Sometimes when one doesn't work or works intermittently due to capacitor leakage, cleaning it alleviates the problems (at least for awhile) by removing the electrolyte, which is a conductive and corrosive material that shorts out and corrodes any components it comes in contact with. It's already dead, so there's not much to lose by cleaning it.
I hope this helps!
c