FCP Projects turned into NO DATA compound clips

Where are Backups configured to be saved? Open the original library on your Desktop, select the library in the sidebar, then in the Inspector pane, click Modify Settings in Storage Location. By default they're saved in ~/Movies/Final Cut Backups/ but maybe they were saved somewhere else and you can recover a more recent backup.

Sorry to hear that. You should check the other FCP backups to make sure they have reasonable backup dates. If you find anomalies, I'd reset FCP settings in case that's what causing backups not to work. Hold command and option while launching FCP. It will open the default Untitled library. Reopen the library you were working on and set your preferences back to the way you like them (turn off background rendering, etc.)

In fact, I'd reset FCP settings anyway since it crashed during the library move. After the Settings reset, try to reopen the desktop library.

As a last ditch effort with nothing to lose, you could duplicate the desktop library as a backup, then step inside this backup (control- or right-click and choose Show Package Contents). Then move CurrentVersion.flexolibrary and Settings.plist files to the trash. Launch FCP, open this backup library and see if anything is better. I'm not optimistic but it's worth a shot. Maybe others will have other things to try.