Unable to download Complete Set of Content

Check, if you accepted GarageBand 10, if it came preinstalled on your Mac, see this link:

GarageBand for Mac (v10.0): Unable to complete in-app purchase

"unable to complete download, check your internet connection"

This waning can also mean, that a firewall or antivirus software is interfering. Disable all firewalls like Little Snitch and try again, or boot into Safe Mode to disable all non-standard system extensions, see: Mac OS X: Starting up in Safe Mode

Are you trying the download from an account with administrator privileges? That is essential for making system wide installations. If you are using a regular user account and not an admin account, switch to an administrator account.

Perhaps your GarageBand preferences files are corrupted. Remove these files from your User Library to a folder on your Desktop:

~/Library/Containers/com.apple.garageband10/

~/Library/Preferences/com.apple.garageband.plist

~/Library/Caches/garageband

Quit GarageBand, then remove the files to a folder on the Desktop and restart the computer, before trying again to open GarageBand.

Your profile signature say MacOS X 10.7.5, but since you bought the in-app purchase, I assume you are using GarageBand 10 on Mavericks?

You user library may still be hidden, as is the default in Mavericks: To open your hidden user library:

• Select the "Home" folder icon (the little house) in the Finder's sidebar and press the key combination ⌘J to open the "view options".
• Enable "Show Library Folder".
• Then open the Home folder and open the Library folder inside and navigate to the Preferences, Caches, or Containers folder. Remove these folders completely - don't leave anything inside: ~/Library/Containers/com.apple.garageband10/,
  ~/Library/Caches/garageband .