As the error says you need to copy System.Data.SQLite.DLL from the Desktop folder (in the SQL library zip) to your application folder.
The zip file includes two folders.
Under the Desktop folder there is the desktop dll: System.data.sqlite.dll - 568k.
The 450k file is the device file.
I recommend you to delete all the System.data.sqlite.dll files.
Download it again, and copy the 568k one to c:\Program files\Anywhere Software\Basic4ppc Desktop. (not the libraries folder)