The computer has lost it's link to the System folder. There are a few options to try.
Restart the computer while holding down the Option key. This will tell the computer to look for bootable drives. If it finds your normal startup disk, select let, then click the right pointing arrow to boot up the computer. Now open up System Preferences> System> and select your normal Startup OS as the default startup disk.
Reset your PRAM. Press and hold down the Command Option P R keys while starting your computer. You will hear the startup chime. continue holding down those keys until you hear the startup chime a second time. Release the keys. If the computer restarts, you will need to reset your Date and Time. It might be time to replace your PRAM battery. The G5 iMacs require a 3 volt CR2032 lithium watch/camera battery like below:
You can find these batteries at Walmart, Kmart, Target, most local drugstore chains, for between $3-$5, or at Radio Shack for $12-$20.
If you have any G5 iMac model EXCEPT the iSight version, you can probably do the battery install yourself. Watch this video on upgrading your iMac's RAM to show you how to remove the back of your iMac, if you don't already know how:
While you have the back off, use a can of compressed air to blow the dust out the vents at the bottom of the iMac, the fans, and anywhere else you can. Also inspect the 28-30 capacitors on the logic board. Look for dark spots, if they look puffy or swollen, or leaks.
Reset the SMC by removing all cables (USB, Firewire, Ethernet, Modem, Power cord) from the back of your computer. Let it sit for one minute. Press and hold the power on button on the back of the iMac while plugging in the power cord. Release the power on button. Count to five, the press the power on button again.
Place your original, came with the iMac when purchased install disk, into the slot on the iMac, press and hold the C key while pressing the power on button on the back of the computer. (If you have upgraded your OS from when you purchased your iMac, example your iMac came with OS 10.3 installed, and you're now using OS 10.5, then use the OS 10.5 Retail Install disk that you had used to upgrade your OS instead of the original, came with the iMac disk.)
Continue holding the C key until you see the OS starting to load. DO NOT do an OS installation. At the top Menu bar, select Utilities or Utility, and pull down to Disk Utility. On the left side of the window that opens,select your normal OS drive. Click First Aid at the top middle of the window if it isn't already selected. Click Repair Disk from the lower right area of the window. When that is done, click Repair Permissions to the left of the Repair Disk button you clicked earlier.
When that is done, quit Disk Utility. From the top Menu bar (I think its under Utilities) select the Start Up Manager, and choose your normal boot volume as the startup disk. Restart the computer. If successful, and you've rebooted from your normal startup disk, eject the install DVD/CD, and you're good to go.