Hi Rocky,
I solved my problem by contacting Skype directly. They have very good support for linux. First they told me to remove skype in terminal, using the following command:
sudo dpkg -P Skype
But this did not work. I was able to remove skype using the package-manager, then to install the correct version using the same. None of my conversations survived, but that is of secondary importance.
Thank you for your help on this one.
* I must qualify my statement: Skype is workig again, but I have not tried the audio. I shall do so (and report back) as soon as mint is running again.
OK, due to other technical problems, I have had to reinstall linux mint on my hard drive. This time I went into the system settings first thing and (completely perchance) clicked on Audio. I discovered there that I can choose both input and output to be default, HDA, pulse, or something else. I chose the settings to fit my settings on skype, and lo and behold, I had no trouble with skype at all.
So here is what I did: menu->control center->(hardware

Audio->
Then i set playback to "automatically recognise" and record to "pulse audio server". Then I tried out skype and it worked. I do not know why I was being so stubborn about not understanding things before, but now everything is working. I hope helping me with this was not a total waste of time for you.