Paul,
You might want to try some running some SQL like this
insert into new_table select col1, col2, col3, col4 from old_table
this will take whichever 4 columns you want to keep from your old table and insert them into the columns in your new table. Just make sure you put the columns in the select statement in the correct order.
Another option would be the SELECT INTO statement.
If you have created a new DB altogether, you can just import your old data as is into the new db and just ditch the table after the select is done.
Hope that helps, I know what a pain it is to change your DB structure and have to update the data.