Chosen Solution
I have some weird issues. It works fine, it boots up and runs great, but the fan is constantly on full blast, its not blowing out hot air. When it first boots up the fans are quiet. When I try to shutdown or reboot the system it goes through all the steps of shutting down, but the screen stays black, wont ever reboot or shut down. I think I have reset the SMU on this model by unplugging everything, waited 10 seconds (or more) held the power button down while I plugged it in and then released the power button and powered it on, boots into OSX no problems or issues. Power supply has been replaced. Oh and another side note, when the system has power unplugged from it, it loses the time and date constantly. I checked the battery and it was putting out the correct voltage. Update Hey guys, sorry it took so ling to answer back. I finally got a hold of a 10.5 dvd. No issues with date/time of fan spinning up like crazy. So that’s what my problem was the whole time was wrong OS. Thanks again for the help :)
On this age machine you probably should replace the thermal paste. BTW that’s an advanced DIY so you might need some help. That a fan is constantly running full blast means something is overheating and the “default fix” is to run the corresponding fan at MAX to reduce chance of component damage from over heating. It could be your CPU or the GPU that is overheating. Running AHT should report which component is hot. A fan app might also catch this. As to the black screen hang/no reboot. If you have peripherals attached - try putting them away (eject mounted volumes) and powering off or unplugging them before shutting down. You might have a failing/misbehaving peripheral. If this Answer is helpful please remember to return and mark it Accepted.
Loosing the date and time (also your printing is probably dropping off line) means your PRAM battery is gone, even if it is reading the correct voltage. I’d replace it. I’d first remove the fans and see if the vents are clogged, or course machead has a good idea about replacing the thermal paste. Here’s how to remove the CPU fan: iMac G5 20" Model A1076 Right Fan Replacement