I've just resurrected mine, I've been curating it for 15 years thinking it was bust - turned out to have been a simple mechanical case design fault.
The power button is an almost friction-fit in the case, the mfrs may have incorporated a trace of lube into the power button aperture when new? Who knows, this problem appeared, sometime it would boot, sometimes it wouldn't, then it wouldn't boot at all.
I took it to the repair shop, they were able to boot it successfully several times a day. I collected it, phoned them when it wouldn't boot, was told that it was very hard to diagnose an intermittent fault and I could replace various components - all of which cost more than a new Pentium 4 ... I jumped ship and never looked back until this year.
So - power button. It could be that simple. Press it too hard and nothing happens.
Try pressing it oh! so gently, it only needs to make the briefest, gentlest contact to illuminate the button.
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As a matter of interest, when did you buy your G3 and how much did it cost? My system cost c. £4,500 /$6300 then, around
£5450 / $7600 today, with upgraded memory, video card, SCSI card, plus scanner, printer, Zip drive, CD-burner and unlimited high-end software - Photoshop, Illustrator, Premier, Quark, Fontographer etc etc etc, all needing no serial numbers and in most cases no installation just copy/paste. I still have them on CD.