I tried one of the drives (same one that did not work on this PC) on another PC also running Win 7 - I was able to access Properties and Format under Windows Explorer so it appears to be a problem with something on this particular PC.
So it looks like the problem is not with the drives themselves.
I am running Bitdefender Total Security 2013 as my antimalware program. I disabled both the firewall and the antivirus - still no joy.
The problem appears then to be something that is running on this PC that is not running on the other PC - or vice versa - or a particular setting somewhere.
This stuff can really make you crazy.