it should be like this
SqlCommand command = new SqlCommand("IF NOT EXISTS(SELECT (FullName) FROM [Staff] WHERE [FullName] = @FullName) " +
"INSERT INTO [Staff] ([Username], [FullName], [Location], [TimeOfLastUpdate]) VALUES (@Username, @FullName, @Location, @TimeOfLastUpdate) " +
"else" +
" UPDATE [Staff] SET [Location] = @Location, [TimeOfLastUpdate] = @TimeOfLastUpdate WHERE [FullName] = @FullName ", con);
I added the ending parantheses after your EXISTS and a couple of spacing issues around "else"