It looks like my installation of TortoiseSVN is becoming unravelled and I can no longer perform a checkout into a fresh directory. Doing things in directories that have already been checked out still seems to work.
There are many hits on Google for this problem:
http://tortoisesvn.tigris.org/ds/viewMessage.do?dsForumId=4061&viewType=browseAll&dsMessageId=2329509
http://www.webtechquery.com/index.php/2010/11/tortoiseproc-launch-failed/
http://groups.google.com/group/tortoisesvn/browse_thread/thread/506470578048be52?pli=1
All of which lead to the same solution of just doing a reinstall, apparently a reinstall with a laborious cleanup.
However, nobody mentioned an obvious workaround which I tried successfully:
From one of my checked out directories where Tortoise still works, I called up the repo-browser. From that directory, I selected the folder that I wanted to check out and from a right-click selected "Check out" from there it let me enter the location that I was trying to put the new checkout into and it worked fine. This keeps me going for now until the unlikely day that I have time to wipe TortoiseSVN's butt for it.