Here is a simple way to ensure default permissions to be restored on home folders :
- Restart your Mac
- At startup chime, press cmd+R to start on Mountain Lion Recovery Partition
- Once on recovery desktop, from the menu bar, select Utilities > Terminal
- Once Terminal opened, type in "resetpassword" command + Enter ... a window entitled "Reset Password" will be opened
- Within that window, select your user profile from the drop box
- At the bottom of that window, you'll find a "Reset Home Folder Permissions and ACLs" section with a "Reset" button
- This will reset your entire home folder to the default permission scheme, this can take time depending on home folder contents
- Once finished, quit all properly and restart your mac normally
Hope this can help.
That was my next suggestion, since you can't seem to sudo.
However, I'm not sure if it will affect that folder you put on the Desktop.
Additionally, you will need to reset all of your sharing settings.
If that doesn't work, I can only think of using single-user mode to give you permission to that folder.
Why not Get Info on that Music folder and see if locked is checked?
All of the home folders with icon designs have ACL placed on them during the initial OS X account setup.
The folders within Music (e.g. GarageBand, iTunes) do not have any ACL set on them. Inside the iTunes folder, only iTunes Library.itl and sentinel (hidden) have ACL set.