Panel content page not displaying correctly after restoring backup on different server
First, before doing anything else, try clearing all the Drupal caches.

Then, if that doesn't do the trick, you need to make sure that you restore your files as well as your database.  Adaptivetheme and Panels both save some of their settings in files (for example, Adaptivetheme saves the color information of the theme); if you restore the database without the files, your site will behave strangely until you restore the files as well.

Alternately, if for some reason you do not have a copy of the files, you can re-save the theme settings by going to Appearance -> Theme name -> and then scrolling down to the bottom of the page and clicking "Save," which will cause Drupal to regenerate the theme files.