I have a Dell Dimension 9200 that will not boot up, no lights light up on the front panel. I changed the power supply & nothing has changed. I pulled the I/O panel to test the switch but can't see the connections in the ribbon that is connected to the panel. I'm sure if it the switch or not. The owner was having a problem with the PC not starting up all the time so after letting it set a while they tried booting it up & it did so they left it on & never shut it off until it died & now nothing. I'm at a lose & really not a Dell fan.
As you guessed, it is probably the switch at the end of the flat ribbon cable attached to a mini pc board at the front panel of the computer. You can try taking this sub-assembly out and look for the through hole solder joints that secure the round switch. Use a screw driver and short out the switch connections and try and start the computer. If it works fine, then rewire an auxiliary (momentary) switch to take the place of the Dell start button. It is challenging, but it can be done and worth a try.