OK. It appears that the issue might be resolved. I googled this :"Repair Internet Explorer 9" and got to a MS websbsite where MS makes a number of suggestions. One of them at the beginning was to uste "Fix it". Though I am not too fond of this Fix it, I tried it and it had no adverse effect - so far.
I also ran the program to delete Temp. Files, restarted after hinishing it, and had no problem to open the problem website mentioned here.
I am not saying that the issue is finally resolved but I have to watch it for a a while.