I'd lay pretty good odds that you've got the bane of all vine crops: squash borers.  They're moth larvae that tunnel into stems and hollow them out, leaving a sawdust-like pulp.   There is usually only one borer per vine, although that's all it takes to kill a plant.  If you look very closely, you'll recognize him as a white caterpillar about an inch long and a quarter inch wide.  If you catch the problem in time, you can try injecting insecticide into the hollowed out spots, then mounding up the dirt around the damaged stem; it may be able to reroot if the damage hasn't gone too far.  If you're like me though, you probably only discovered the problem when what was a beautiful thriving plant one day became a limp, dying mess the next.  Later in the season pumpkin stems usually toughen up enough to resist them, but since yours were just starting to run, I'll bet the moths found your garden a little early this year.
One thing you can try is a companion planting trick: plant a couple of icicle radishes near your squash family crops.  Don't pull the radishes, just let them continue to grow and go to seed.  The radishes will help repel the borer moths.  Planting onions or other alliums nearby can help, too; the moths don't like the smell.