Do you have the SQLite.Interop.dll file in your modeler directory? There should be one in the /modeler/x86 and /modeler/x64 directories.
If they are there, then I'm wondering if perhaps you have an incompatible version of SQLLite.Interop.dll registered and getting loaded instead. Can you remove the SQLLite installation at C:\Program Files\System.Data.SQLite\?