If you UNPLUG the Motherboard power cable (20-pin), you should be able to test the power supply itself directly. If you SHORT (connect the two of them with a single wire) the green cable with any of the black cables, the PSU should turn on and all devices attached to it (CD-ROM/DVD, HDD, etc) should all power on as well when they receive power. You can then read all the voltages from all the pins on the 20-pin cable with a digital multi-meter. Please do not shock yourself doing this. At my old job, we had an actual PSU testing device that would tell you all of the voltage rails, test out Molex, SATA, even the 4/8 pin CPU and 6-8 pin PCI-E cables and let you know if anything was out-of-spec. Very nice. It also automatically powered the thing on by shorting that green wire to ground as soon as you plugged it in.
Once you've verified the PSU is fine, then let's look at the MB. Plug it back into the PSU, then what I would do is instead of relying on your switch, I'd find the two pins that are marked for the Power Switch and short them directly with a phillips or flat-head screwdriver - taking care not to touch any other pins. As soon as you short the two pins, the system is supposed to power on.
If that doesn't work, start poking around for culprits. I'd take the CPU out, then reseat it. It's a Slot-1, so it'll be tricky, but it needs to be fully seated. We don't even care about the fan yet. If the CPU is not in the socket, it's quite possible that the system won't power on at all anyway.
As part of my testing, I'd also take EVERYTHING off of the MB except the CPU, power cables, and some kind of speaker-header so you can get beep codes. See if you get anything. If so, then put 1 stick of RAM back in, power on again, note beep codes. If good, then put your graphics card back in and hook the monitor up and turn it back on. If you get power still, then at least you'll have a beep code AND a screen display. It should be reporting the 1 stick of RAM and NO drives (because we unplugged all the drives). Work your way one device at a time until something either fails (causes the system to not power on) or you're fully stocked and powering on (because all of the previous steps may have fixed the issue).
Since it's a power issue of some type, start with the FIRST AREA and follow the power from the wall all the way until you have a complete system. First, test the PSU (getting its power from the wall), then the MB and CPU combo (point of distribution), then the RAM, then the VGA card, then a HDD, then Sound, CD-ROM, network, etc. Work your way from the wall socket on out.