If you can get an external 3,5" HDD enclosure, I'd take out the disk(s) that are not backed up, and back them up first on another computer. (You actually should have had bootable backups in the first place, but it's never too late to learn, you learn the hard way ;-)
I could be wrong but I still have a strong feeling that it's a PSU problem.
Good news: if your fans still work, the PSU is not blown (yet). I suspect that dust could cause the symptoms you're seeing.
You have access to an air compressor? Preferably one that has a moist filter. (Canned air is way too expensive, but an option if you don't know anybody with a decent air compressor. Pressure of a can is lower too)
I'd first try to blow it out without disassembly. The PSU is on the bottom, so blow through the frontgrid at the bottom.
You won't be able to get all the dust out, but it might work allready.
I recommend you do this outside, and be surprised by the huge dustcloud that comes out, and be glad you didn't do it in your house.
If that didn't work, I would disassemble your G5, take the PSU out, blow it out more thoroughly, by opening the case of the PSU.
You will find links to guides how to do this in the thread I mentioned in my previous post.