Pretty difficult to know how to resolve without access as it is something site specific.
When you loaded the latest jD version do you remember if you used the Manage - Install or Manage- Update?Before any of the following pllease make a site backup - just in case!
Perhaps the upgrade got interupted somehow as it sounds like that, so you could retry the jD upgrade again by Extensions - Manage - Install(not Update) - Upload Package file.
If that fails then you could try the Install from Folder method See link below for details on that method.http://www.jdownloads.net/documentations/item/how-to-install-update
Another scheme is to Uninstall jD. When doing so jD will ask if you want to remove the Database and Download Files and Images. Say No to keep all of them.