What type of data is in your map package? By default the Local Server deployment created when you build your project contains only the default/minimum resources required. Some data formats, such as shapefiles, raster data, and enterprise geodatabase data require you to specify additional deployment options in the deployment config file. For more information see Create a Local Server deployment—ArcGIS Runtime SDK for .NET (WPF) | ArcGIS for Developers.
As a quick test, I'd recommend changing `<Package name="Local Server" enabled="true">` to `<Package name="Local Server" enabled="false">`. And then running a Rebuild or Clean/Build on your project. That will cause the API to use the central installation of the Local Server SDK in `%ProgramFiles(x86)%\ArcGIS SDKs\LocalServer100.1`, where all the resources are present. Once you have confirmed that works, then read the doc above to determine which deployment option(s) you need.