Just repaired my iMac G5 with complete boot failure, it all came down to capacitors, there was an industry wide use of sub standard/sub spec capacitors at the time the imac G5 was manufactured, due to a manufacturer using a capacitor recipe missing one ingredient, This caused the imac G5’s to fail at a much faster rate than they should have done, I had to replace half the capacitors in the power supply and 5 of the higher rated capacitors nearest the power supplies internal vent onto the logic board once this repair was affected, my machine worked perfectly.

take the cover of the back of you imac G5 and see whether your imac version has some led diagnostic lights and check whether the power diagnostic led light lights up properly when started, there are tutorials for this on the web also a light there that indicates whether gpu is communicating with the display properly. all led internal green lights should light up, apart from the right hand one of the four.

with your dar screen sleep light on symptoms it seems quite likely a surface mount BGA graphics chip failure, but to be honest it could also be a capacitor related issue, if your not into stripping the machine down and soldering capacitors then the machine for you is probably a right off, just try a pram reset boot before giving up, I had similar sleep light no boot scenario on a macbook pro, and a stripdown got it booting again.

the power supply in the imac G5 gets very hot and has no fan of its own and is dependant on the one internal motherboard fan, there is also no temp sensor for the power supply to give you an indicator as to how hot its getting, I feel the the heat venting from the overheating power supply internally is what cooked the capacitors nearest it, this is a flaw in the design of this machine.