If you want to insulate inside the house but don't want to remove the old wall, here's what you should do:
-- Make a couple of exploratory holes in the wall (don't worry about being neat, you're going to cover the wall anyway) to find out how much insulation is in the wall and if there is a good vapour barrier.
-- If there is a good vapour barrier, use a drill, or ice pick, to punch holes in every wall cavity, and destroy the barrier -- we don't want two vapour barriers on the same wall.
-- If there is twice as much insulation inside the wall as you are going to put on the wall, you may put the new polyethylene vapour barrier directly on the wall -- after having brought forward the electrical boxes. This will provide a good air barrier behind the boxes and a good vapour barrier over the entire wall.
-- If there is NOT twice as much insulation inside the wall as you are going to add on the wall, put the air/vapour barrier on the warm-in-winter side of the new insulation.
-- If the wall is solid and flat, you can glue any of the polystyrene foam panels directly to the wall. Drywall or masonite type prefinished panels can be glued directly to the foam AND nailed top and bottom to the wall (for fire safety). (search keyword "basement" for the title "BASEMENT: INTERIOR OR EXTERIOR INSULATION?")
-- You can build a whole new wall frame away from the wall, or nail vertical or horizontal strapping directly to the old wall, then insulate with batts and finish it.
-- The windows and doors pose the greatest challenge with a thicker wall, and should be planned ahead. Build a good air/vapour barrier right to the window and door frames. (search keyword "sealing" for the title "WHERE SHOULD I SEAL AND HOW?")