One important detail in resolving this issue was remembering that I wanted to keep my workspace. When I decided to start from scratch, I backed up the workspace, and then copied over only the directories that I needed, instead of the entire workspace as I had been doing.
The result of starting fresh is that some hidden files residing in the old workspace were not longer present and the triggers for installing the connector executed properly.
Go to the marketplace and search for Subclipse (or another tool) and install it. Next time you open the Team Synchronizing perspective you will have SVN support (not only Git and CVS anymore). You will be able to add SVN repositories as usual in SVN Repository Exploring perspective.
Note for anyone having strange Eclipse plugin install/update problems under Windows: if your normal Windows login does not have Administrator privileges (for security it should not) then Eclipse plugin install/update can break unexpectedly due to file permissions.
An example (misleading) error message when attempting to install SVN connectors is:
No repository found containing: org.eclipse.update.feature,org.polarion.eclipse.team.svn.connector,3.0.1.I20130507-1700
In this case, always perform Eclipse plugin install/update as an Administrator and the above-mentioned problems vanish. I thought I should share this here because the Eclipse error messages can lead you in completely the wrong direction.