My Desktop seems to be “locked”. How to fix this

Since you haven't used ls -le as recommended, we don't know what the access control list looks like, but there might be something going on there that is preventing you from being able to write the files. The fact that a newly created user CAN edit the files makes me even more suspicious.

This command will remove ALL access control list entries from the folder and all its subfolders and files:

sudo chmod -RN path/to/folder/containing/files

Once you've cleared the access control list, try resetting the ownership like so:

sudo chown -R ulrikdamn:staff path/to/folder/containing/files

Now grant permissions like so:

sudo chmod -R u+rwX,g+rX,o+rX path/to/folder/containing/files

This gives you full read/write permissions. The "staff" group and all other users get full read permissions. Using an uppercase X, sets the execute bit for all directories within the tree, but leaves the execute bit for regular files as is.

Lowercase x would set the execute bit for all folders AND files. The execute bit must be set for a directory in order to read its contents. If you'd like to give write permissions to the group or others, switch out for g+rwX or o+rwX as necessary in the last command.

Here I'm passing in a folder path. If you want to pass in a single file, just remove the -R from each command. The R makes the command recursive, applying it to an entire directory tree. Without it, the command will modify the permissions for a single file or folder passed in.

The first step I would recommend is to try resetting your home folder permissions with the Reset Password utility in Lion Recovery. (Despite the name of the utility, you won't actually be resetting any passwords.)

Resetting the home folder permissions with the Reset Password utility will reset both the owner and the permissions.

1. Restart your Mac holding ⌘+R to boot into Lion Recovery, which will bring you to the Repair Utilities screen.

2. Open Terminal from the Utilities menu.

3. In Terminal, enter resetpassword to open the Reset Password utility.

4. Choose your hard drive icon at the top, then choose your user from the drop-down menu below. Do not reset the password here.

5. At the bottom of the window, under "Reset Home Directory Permissions and ACLs", click the "Reset" button. This may take awhile if you have a lot of files in your home folder.

This should solve your permissions problems for most apps. However, it's possible you may have a few apps which had saved files with special permissions that are different from the user's default permissions (like preferences or application support files). For those apps, you may need to delete their preferences or reinstall the app.

If resetting your home folder permissions doesn't work, then you may need to try restoring from a backup or transferring your data to an external drive.