After some experimentation, I discovered that the Intego firewall in VirusBarrier X6 views the App Store as spyware and silently blocks some access. This happens even if you set the Intego anti-spyware entry for App Store to allow outgoing connections for undefined port behavior.
The symptom that appears is that the App Store page displays but clicking on login or "do something" links do nothing and show no error message.
The cure is to open VirusBarrier X6, go to the "Privacy" part of the dashboard, and turn off "Spyware protection." Then do your App Store thing and after completion turn "Spyware protection" back on.
Other firewalls may do the same thing, but Intego is the one I run. I don't know what it is about the App Store that the firewall doesn't like, but if it doesn't like it I don't either :-)
Thanks for the tips. But... it's been pointed out long ago that VirusBarrier X6 does more harm for you computer than good. So I'm not sure this advice is going to help much. It's been responsible for probably more issues on macs than Norton...