I did a 7up with one of my boys a couple years ago. It was certainly not a professional job, but turned out well for what we wanted it to be. Bought it for $40 at a garage sale and turned it into a keepsake my son will take with him when he leaves the house some day. We used a dremel tool to cut the spot welds out and separate the lid from its inner liner. It was the only way we could get access to try to straighten out the dents in it. We put it back together by filling it with low expansion foam. Not as strong a hold as the welds, but it essentially "glued" the 2 pieces together. Holds fine since the piece will be used only for display purposes. Our paint was just rattle can, and we left the inner liner with the original galvanized finish. The inner liner for the cooler is held in place by the compression fitting along the top edge. You can carefully bend this out with a flat blade putty knife and slide the liner out. All the metal pieces can be polished up to look pretty nice. I looked all over for replacement corner pieces, but could not find a source.
I have the same Pepsi version of the cooler in pieces now. My youngest is doing that one with me. It's sort of a compromise I have with my wife. When I pick up a new item, I redo it as a father/son project. That item then becomes theirs. It ensures her that down the road it will eventually leave the house. The pics below show what it looked like when we got it. The lid was smashed and had a hole rusted all the way through it. We took it apart, banged out the dents, did our best bondo job (still learning that process) and just painted it last weekend. Not sure if the color is what we want, may not be dark enough to match the original close enough. Working on the cooler body now, trying to figure out how to do the Pepsi stencil for the embossing. If anyone knows where new corner pieces can be found, would love to know where.
I took several pics of the 7UP project and saved them to a photobucket album. You can look at it here if you want to see how we took it apart and put it back together. Like I said, this is an amateur level restoration, but it may have some useful pics.
http://s1230.photobucket.com/user/ilikecoinop/slideshow/Jakes%20Picnic%20Cooler