For whatever unfathonable reason, although almost all PCs have been 64-bit for years, the new Skype must have the 32 bit pulse audio libraries to work. The rest of the new Skype is drastically improved over the previous Linux versions.
apt-get install libpulse0:i386
I found this at http://askubuntu.com/questions/312679/skype-is-not-using-pulseaudio. There were many other sites that proposed solutions, but the one that worked is the above — add the 32-bit libraries: skype won’t use the natural 64-bit libraries.