Moving iMovie 08 projects will not be as simple as previous versions. In previous version you had a project file that was self contained. In the new version things get tricky.
iMovie 08 relies on three folders within a users Movies folder. (The 'iMovie Events' folder can have it's name on the root of other drives too.) Two of those folders are important; 'iMovie Events' and 'iMovie Projects'. I'll now refer to them as iME and iMP. The third folder is 'iMovie Sharing', which you'll find content in when using the fixed Sharing export options.
Keep in mind I haven't had to try what I'm about to suggest. It just makes sense though when thinking of the standard install.
First of course you should be running the same or newer version of iMovie on the computer you are copying to.
What you want to try is to move the appropriate event names you are using content from and the project name from the iME & iMP folders from the first computer to the same location on the second computer. Do not alter any of the names. I would then expect iMovie to start as expected and be able to use that content and project.
Sample, given names 'Event1' and 'Project1' and user 'mickbab' on the first computer and 'xstep' on the second computer.
The first computer will have;
~/mickbab/Movies/iMovie Events/Event1
~/mickbab/Movies/iMovie Projects/Project1.rcproject
You want to copy those two items to the new computer to;
~/xstep/Movies/iMovie Events/Event1
~/xstep/Movies/iMovie Projects/Project1.rcproject
One possible issue might be if you are using images from iPhoto. I don't think the copy will find the original file if needed, although it will have a self contained image it copied originally. You may or may not see quality issues with this copy. I have my own questions about possible quality issues that I don't want to get into here. You can investigate further by opening a project file that uses stills and open the 'Still Images' file via QuickTime.