iMovie 7.1 (the latest update to the version of iMovie in iLife '08) will only run on G5 Macs or later. Or so it seems. There's a way to hack it to work on G4s as well. Simply add a patch to the program's contents, as explained here.
[kirkmc adds: Untested. Use at your own risk, etc.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20070928151807481