Peat/perlite is generally not recommended because it's too dense. It doesn't drain quickly, which isn't a terrible thing until you take into account that it also doesn't hold much air, which causes it to smother roots that don't enjoy waterlogged conditions. The dark color conspires with the above properties to make it warm quickly in the sun, which is one more thing that Darlingtonia really dislike. I use peat and perlite with my plants, but I usually mix in big chunks of pumice and live Sphagnum. At the very least, more perlite than peat as the others have said.
I know it looks like it's hurting, ieat, but I don't think it's a total loss. Keep the pot in water at all times, but it might be good to keep the water level shallow as well. You might try putting it in a large open-mouthed jar or a large plastic bag with the mouth open. Extra humidity may help - I don't think you should put it in a closed container like the death cube though. If you can add pumice, coarse perlite, or some other large aggregate into the mix, then the sooner you do it the better. But with care you can make it work how it is. A larger pot will work wonders, as well - Darlingtonia like pots where they can spread out wide.
Also, it might help us to know a few more details. When did you get it? When did you repot it? How long has it been out of the cube? Is it outdoors, or inside on a windowsill, or under lights? How are you watering, and what are the temperature/humidity ranges it's experiencing?
~Joe