The file that iWeb needs to create and edit a website is called Domain.sties2. It's located by default in your Home/Library/Application Support/iWeb folder. If you don't have that file you'll have to rebuilt the site from scratch.
If you have the Domain file on the new computer you may need this application to open it for the first time:
To open your domain file in Lion, Mountain Lion, Mavericks or Yosemite or to switch between multiple domain files Cyclosaurus has provided us with the following script that you can make into an Applescript application with Script Editor. Open Script Editor, copy and paste the script below into Script Editor's window and save as an application.
do shell script"/usr/bin/defaults write com.apple.iWeb iWebDefaultsDocumentPath -boolean no"
delay 1
tell application "iWeb" to activate
You can download an already compiled version with this link: iWeb Switch Domain.
Just launch the application, find and select the domain file in your Home/Library/Application Support/iWeb folder that you want to open and it will open with iWeb. It modifies the iWeb preference file each time it's launched so one can switch between domain files.
WARNING: iWeb Switch Domain will overwrite an existing Domain.sites2 file if you select to create a new domain in the same folder. So rename your domain files once they've been created to something other than the default name.
NOTE: In Lion and Mountain Lion the Home/Library folder is now invisible. To make it permanently visible in Lion or Mt. Lion enter the following in the Terminal application window: chflags nohidden ~/Library and press the Return key - 10.7: Un-hide the User Library folder.
For Mavericks and Yosemite go to your Home folder and use the View ➙ Show View Options menu to bring the this window:
If you don't have the Domain file and need to start over from scratch this would be a good time to migrate over to a modern, supported web development application. One that may have migrated to because it is so very much like iWeb is EverWeb.