[Arran]

 I think that the sides were toned, they are just faded to a large extent thanks to the moisture damage, they likely matched that molding above the dial. It's poplar, or some sort of bland junk wood, so it would be normal for it to be covered with a coloured finish. The joints are coming apart for much the same reason, though pre war cabinets used a lot of hide glue which tends to crystalize and let go sometimes anyhow. There is someone on here that three or more Philco PT-6s like this so they could answer as to whether that stump or burl walnut is real, I think it is otherwise half of it woudl be gone by now much like the sides.
If the cabinet is falling apart I would take your time with it, knock it apart, reglue a section at a time, and invest or borrow lots of clamps to help with it, bar and pipe clamps. I would leave the old finish on before gluing it up, it can be useful for avoiding glue stains, or at the very least you won't have to clean up twice. One problem you may run into is warping, if it got damp enough for the bottom or side to delaminate the edges of each board may have moved a bit, sometimes you have to recreate damaged pieces, or run the damaged ones through a saw to square up the edges and then add filler strips.
Regards
Arran