That sure looks like vine borer damage to me. My condolences. The little black things are not the vine borers, they are icky white grubs that could well still be in the vine.

If you dig it out, and kill it, you might be able to bury the damaged stem and have it grow roots and recover, but in my experience, its a goner.

Thanks so much for your help! Though of course definitely bad news!!! I'm torn now between trying trying to cut it out (of all 10 plants) or pulling those plants out and starting over. I'm trying to grow pumpkins for Halloween with my kids and according to seed packets I have enough time if I sow now. What do you advise? Thanks much again :)

I'd use spinosad instead of sevin. Although it's been touted for years as OK to place on veggies, sevin is horrible. Of course, if you're not going to make pies out of the pumpkin,
it's alright, still not good for environment.
This link will tell you about spinosad and controlling squash vine borer, scroll down to chemical control:
http://www.extension.org/pages/65684/biology-and-management-of-squash-vine-borer-in-organic-farming-systems#.U5T0ifldXNl

Also, link to the fallacy of using sevin dust:
http://foodtruthfreedom.wordpress.com/2012/03/14/why-grow-vegetables-and-put-poison-on-them/

Either way, good luck with your pumpkins. A great project the kids will always remember :)