Go to Edit >> Catalog Settings >> General (tab)
Click the button "Show" and you should be taken to the catalog folder in Finder.
Look for your named catalog with the ending.lrcat and double-click on it to launch.
Use your operating system to search all hard disks for files whose name ends with .LRCAT
Double-click on the .LRCAT files found to open them in Lightroom.
Where did you place the catalog file and backups? On an external drive? Mac OS X is known for not initializing, Seeing, external drives right away. Sometimes it take a few seconds to a minute or more for OS X to See an external drive even if it was connected when the system started up.
This is especially true for externals that use the USB connection to power up the drive.