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If you have a Firewire hard drive it should be able to boot your Mac.
However, usually external hard drives are best served as backup drives because of their reliability. So really if your external is just a backup drive, I would not install anything else on it, and use it as your point for recovery to a new internal drive.
You can force the machine to recognize the external hard drive as a boot volume using the Startup Manager:
http://docs.info.apple.com/article.html?artnum=106178
To make it boot an iMac G4, you need to make sure it is Apple Partition Map formatted (which it would be if you formatted it from your iMac G4 to work with just the iMac G4). If you never formatted it with Disk Utility, then it likely won't be able to have Mac OS X installed on it, as most external hard drives are formatted for the PC by default and are not Mac installer friendly. Unfortunately formatting will erase your hard drive contents. So the questions I have to ask, is the La Cie your soll backup? And was it formatted for the Mac?