Bob,
My "Babylon" problem was blessedly rather simple the way I had stated in my previous post, and a simple solution to it too occurred to me after I read your reply. So this note is to thank you for your prompt reply, and also to let other readers know of the simple solution in the event that they have the same simple "Babylon" problem.
After following your suggestion and checking my browser add-ons for both Firefox --my default browser-- and IE, I found that there were no "Babylon"-related add-ons for either browsers. However, as I had written, Babylon's search web page used to strangely pop up when I opened a new window in either Firefox or IE. Other than that annoyance, I have not noticed any serious problem like a virus infection in my computer through "Babylon." (I have AVG protection.).
It occurred to me to go to Tools > Options > General > Home Page, and look up
the web page link which was already there. I found that Babylon had indeed SOMEHOW sneakily introduced its search link as my Home Page. So I just replaced it with the one which I wanted, and my problem is solved.
Thanks again. You and other moderators at CNET keep doing a marvelous job helping probably thousands of people with their diverse problems.