An easy way to build a very well insulated box: Get a sheet of rigid foam insulation from a builders supply shop (get 2" or 1.5", should be available in 2'x8' or 4'x8'). There is (what is locally called, varies regionally) Super-Tuff R, which is foil faced on both sides. It cuts with any type of hand saw (or a serated longish knife) very easily, making nasty, itchy, fiberglassy, respiratory damage causing dust. So cut outside, long sleeves, dust mask (a must) and gloves if you're tender (most nastiness can be avoided by cutting with a long sharp knife, but it's less easy). Anyway, cut to size 5 pieces, pin them together with some 16d nails and duct tape the whole mess together ( make sure to tape/seal the cut edges so no nasty dust is gonna get scraped off.
Using styrofoam board is much less nasty, just as easy the little foam crumbs are super staticky though. The final result by itself will be better insualtion than most any coolers are I think.
Oh and check the prices, might be cheaper to buy a new cooler.