This looks like a permissions problem - you either don't have read/write permissions to the GarageBand Template files or to the folder, where you want to write the project to. Also your GarageBand Preferences may be corrupted, or GarageBands caches need clearing.
Remove the folder ~/Library/Caches/com.apple.garageband/ from your User Library, or try HangTime's "oddball problems" fix:
As you probably know, the User Library is hidden since Mac OS X Lion.
You can reveal it from the Finder's "Go" menu in the main menu bar:
Finder > Go
Then hold down to options-key ⌥, until Library appears in the drop-down menu. Select it and open the Library.