If the leaves are all dead, it's not going to ripen.

I guess the future is bleak for first melon I have ever grown. I I am leaving it on vine as is until the vine dries out. In the meanwhile I used some sphagnum moss for air layering the vine on a node close to the melon. I had a broken part of a vine root in water recently, so I am thinking if it roots, maybe it will grow some new leaves after potting up the new roots. It is still a good 2-3 months before frost so who knows...

Well, the vine shrivelled, so I had to harvest the melon. It is still very green on the outside. Here is what it looks inside. Not quite sweet enough but edible and mildly sweet.

That's good you salvaged something edible. That's happened to me -- the vines die back (usually from disease of some sort) but I'll pick the melons anyway and see if they're edible. I can deal with subpar cantaloupe/charantais, but not watermelon -- those I end up tossing.

Yes, I am glad it wasn't a complete write off. Considering it was a volunteer from my compost and grew on a 3/4' vine in a pot that got very little sun, I will even call it satisfactory outcome. The experience of growing a melon for the fist time is of course priceless.