I have fixed this problem on my two systems. I forced an update of Joomla by manually installing the current stable version from
www.joomla.org/download.html and downloading v3.4.5. I used the "manage extensions, install" and voila, it worked.
As a minor issue, weblinks then created an error and loaded two instances. I uninstalled both instances and then installed the latest weblinks. This is not the first I have seen on problems for weblinks and I may trash it as I find it creates more troubles than it is worth, at least in my opinion.
After these steps Zapcalendar Pro installed as expected.