Everything looks fine from an environment standpoint (other than your PHP is very old). You shouljd consider upgrading to something still actually supported by the authors of PHP.
Ensure that your account has the close permission.
Go to: Admin panel -> Agents -> Agents: your account
Click on the Access tab
make note of your role.
Go to: Admin panel -> Agents -> Roles
Click on your role.
Click on the Permissions tab
ensure that "Close" is checked.
If that doesn't work then i do not think that you can do anything with them in the UI, and I have no idea why. Perhaps your PHP error logs would shed more light on it.
You can also use your favorite 3rd party SQL editor to connect directly to the database, locate the tickets and manually change the status to closed. To do this you look at the *_ticket table, locate the row, and change the status_id to 3.
