I've been scouring the site and cannot find where the media (videos) are stored. Is there an SQLite database that holds that information?
Media items in the Media Manager list are not actually stored within OpenLP. The videos and audio files remain at their original location, and a link to the file is stored in OpenLP's config settings.
The settings store differs between different OS. On windows, it's located in the registry (HKEY_CURRENT_USER\Software\OpenLP\OpenLP\media). You can export your OpenLP settings (eg for backup) on any OS with File > Export > Settings.
Why are you trying to locate the media store? Something we can help with perhaps?