You may need to, "unhide" the purchase.
Follow the instructions here > Mac App Store: Hiding and unhiding purchases
Try re downloading GB again ...
Open the App Store. From the menu bar click Store > Sign In
Click Purchases from the top of the App Store window.
Select which apps you want to re download. Then right or control click where you see Installed then click Install.
Make sure and use the same Apple ID used for the original purchase.
Might be a corrupted preference file (.plist)
Go to ~/Library/Preferences
Move the com.apple.garageband.plist file to the Trash.
If it crashes again, go to: ~/Library/Caches/com.apple.garageband/Cache.db
Move the Cache.db file from the com.apple.garageband folder to the Trash.
Restart your Mac. Try GB.