Blue screen on iMac G5 after replacing logic board

Try booting from internal hard drive in verbose mode - "apple-v" held down at power on. It may help determine what is causing the boot failure. My suspicion is a graphics system failure, since the install disc is not going to kick in higher graphics modes. The blue screen occurs when the boot transitions from lower level processes to start higher level processes, kick in graphics modes, preferences, etc...

Also, look at the logic board for indications of swollen or burst capacitors.

Unfortunately, it was common for the reworked boards to still fail, even after the capacitor issue was identified (because only the failed caps were replaced on the original reworks, known suspect caps were left on the board if they were still working - causing the board to fail again when they burst later.)