I wouldn't do anything until you've verified there isn't a problem with the front panel assembly.
That's one place where there could be a problem, it's been the same parts this whole time, and if there is a problem there it would either be easy to fix or inexpensive (should be) to replace.
If that's not the problem after all you've been through I would reevaluate whether you want to fix the system or simply replace it.
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I'm working on too many things at once. Pardon me if you've done this already.
Have you tried booting to the BIOS with the drives disconnected? (floppy, optical, and hard drives)
Occasionally a drive will short internally and that will keep the system from booting.
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Replacement might be less expensive than repair:
I occasionally see complete working GX280's go for under $100 on eBay and prices are going down.
The reason is this model was a favorite for corporate contracts (zillions got sold) and most of those contacts rotate the PC's at between 3 and 5 years old which is about GX280's age is right now.
In other words there are LOTS of them for sale right now.
There are even places selling them by the pallet load.
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If you still want to repair at this point I would:
Inspect inside the PSU and on the motherboard closely (with a flashlight) for bloated caps or anything that looks to be getting too hot. (Darkened spots on PCB, burnt looking parts, shinny spots on chips, cracked chips, chips with melting or holes.)
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Look at your south bridge chip closely. If there are any shinny spots (or melted spots or holes/pits) that indicates melting inside. In that case the chip and motherboard are toast.
Usual cause is a bad power supply or a power surge that makes it through the power supply.
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If everything looks okay then next try PSU on a known good motherboard AND check the voltages with a voltmeter. Check with it idle and with it doing something. [Running Memtest and having some drives connected to PSU is probably enough.]
You don't want to see a huge change in voltage from unloaded to loaded. That indicated the PSU is having trouble regulating voltages. I would consider 1/2 volt change at least questionable even if it stays in range. If it goes all the way out of range on any rail it's bad.
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