SMC reset on your iMac ALC G5 is just unplugging everything from the back, wait 10 seconds, then plug in the power cord while simultaneously pressing and holding the power button on the back of the computer.
Release the power button, then press the power button again to start up your iMac.
(
@SGilbert -- no, there's an internal power button near the upper fan, but no reset button on this model
)
But, your iMac seems to function, with a working display, and you get to the desktop in Safe Boot mode?
Apple's Service Diagnostic (ASD version 2.5.8, IIRC.) has an "OSX boot" which tests how the hardware reacts to an operating system. I would run that on your iMac, if you can find the download for that ASD disk. The CDs don't exist for sale sanywhere, as far as I know. You have to find the download (disk image) that makes the CD, and I'm not sure where you could go to find that.
Here's a
page with potential downloads. Scroll about 3/4 down the page for ASD-2.5.8.zip
That's the version you want for your G5 iMac. I didn't try the download to see if it actually links to something (Apple official downloads tend to get removed without warning) This link appears to download a large number of files, so you want to view the results, looking for Apple's file number, which is 693-5964-A. You might also see it listed as Apple Service Diagnostic (ASD) v.2.5.8 -- or something similar. It will explain in the file how to make the CD from the file. (Good luck on that if you want to try)
So, you see --- I suspect that you have a problem on the logic board, or could even be a failing (weak) power supply.