Q: I have 2 iMac G5's that upon starting, will not load anything other than "busy" circle. Is this the logic board?

Could be the LB but also other things less costly, like the hard drive. It could even be as simple as the internal backup battery being dead if the computers have been stored off any power for a while.

Try booting from an optical system disk like the gray one that came with the computer. Insert the disk and restart holding the c key until you see a desktop. That often works if the problem is a dead internal battery. A regular restart then should give you a working computer.

Likewise, you can overcome the effects of the dead battery by holding the four-key combo command option p r while restarting and keep holding until you hear a total of three (3) startup chimes, then let go. If you get a desktop, it's probably the battery.

Another option not related to the battery but one that does some directory cleanup is a safe boot. Hold the SHIFT key down until you either get a desktop or a message saying you are in safe mode.

Let's try these before assuming the worst.