When you install a corrupt skin and DNN dies you can go into the file system under portals/#/skins/ and delete the "YourBadSkinName" subdirectory.  DNN will then recover and display the default skin.

*** Use Sam's solution first ***
I need to write that one down also

The suggestions below are brief but your "support" guy should understand.
I have not actually tested anything I wrote but this is where I would start to fix a similar problem.

You also may want to wait to get a few more suggestions.

1. Backup your whole site.

2.   If different skins are used for the "admin" login and the "host" login try the login that you did not use to upload the skin.
3.   Look at the DNN folder structure under:
          DotNetNuke\Portals\_default\Skins or
          DotNetNuke\Portals\0\Skins
4.   See if you can tell which skin you modifed.
      If you have a recent backup restore just these files.
5.   Look in the DNN_Skins table in the SQL database. (this will be just the Skins table if you did not use a qualifier).
      The skins applied to each Portal along with the associated "admin" or "host" account are found here.
      Change the corrupted skin to one of the others.
        
Be sure to backup your file structure and your DNN SQL database before making any changes.