Only you can decide when to give up, but I am very confused why you are having these issues...
Step 1)
Blow out all dust from the inside with a powerful air compressor (put a small wire in any fans so that they do not rotate (they can over rotate with a strong air blast which is bad for the fan). Heat is the enemy, dust generates heat; also look very closely at all components on the logic board, inspect for burnt (dark areas) also any physical damage like battery acid, or moisture corrosion.
Step 2)
Download the hardware test for the G4 you own from our site, burn a CD and Test it, use the "extended" test on memory, it will take a long time, but we need to start with a baseline of functioning hardware. Age does not matter if it passes all the diagnostics, think of it as new
Also, it may even pay to leave the machine on for 2 hours and test again... Some CPU/RAM/Logic board issues... happen after heating up for a while
http://macos9lives.com/smforum/index.php/board,33.0.htmlStep 3)
Turn off every extension possible and test the configuration, add additional extensions one at a time.
http://macos9lives.com/smforum/index.php/topic,570.0.html