You'll need to install a cMIOS to run Gamecube backups. Go here for a guide with a link to the files you'll need:
http://sites.google.com/site/completesg/gamecube
After that's installed, you should be able to use Neogamma to load your backup disc. If that doesn't work, I believe there's a loader specifically for GC backups, but I've never used one. A google search will turn one up, I'm sure.
Alternatively, you can install the cIOSCORP package, which is a fairly extensive modification of your Wii's system files. The upshot is that it allows you to start backup discs right in the disc channel. I have read about it making life complicated, though. In the interest of completeness:
http://gbatemp.net/index.php?showtopic=188378