That’s a pretty good idea, if you’re sure it’s just the logic board and your hard drive is still OK. And that would probably work, if you manage to find the same model iMac. Then you could use the Migration Assistant with a Firewire or ethernet cable to move all your files and settings to the new iMac when you start it up for the first time, and the files and programs on your new iMac would be nearly identical to your old iMac.
But that method is not going to work with a newer Intel iMac, because your iMac is an older PPC model and the install of OS X on the old hard drive is just for that model. The iMac wouldn’t start up with your old hard drive in it, so you’ll need to find the same older model iMac. And that assumes the hard drive it OK, too.
What might be easier is this: get an universal drive adaptor cable that will let you take the hard drive from the old iMac and plug the drive directly into another iMac like an external USB drive. This cable at the link is listed as working with any hard drive: Newer Technology Universal Drive Adapter. The cable adapts any internal hard drive – with a variety of connections, like IDE, SATA, etc. – into a USB drive that can then be plugged into any USB port.
I’m thinking that because the Migration Assistant works with external drives, you may be able to plug your old drive in with the cable and have the new iMac “see” your old hard drive like it would the old iMac. So when the Migration Assistant asks you if you want to copy information from another Mac, try and select the USB drive, and since it was a bootable drive in the old iMac, and I’m thinking it should work.
If the Migration Assistant doesn’t work when starting your new iMac, or if you’ve already started the new iMac and are already using it, then plug the old drive in – with the cable – and see if the drive will appear as a USB drive. If so, then import your email and photos into Mail and iPhoto using the “Import” command in each program, and then copy your other files over, like documents and other files.