After hours of "live chats" with technical support people from both McAfee and Dell I finally resolved the problem with our new laptop on my own. Well, with a little help from google, an old forum thread on a website called majorgeeks.com and some user called Matacumbie.
I tried to install McAfee the other day since our old one had expired. Everything went nuts. It wouldn't open the McAfee program once it downloaded. Then Windows Media Player wouldn't open either. So I spent a good deal of time both Friday and Saturday nights chatting with technical support from McAfee, and a good deal of today either chatting with Dell Support, or running about a ga-zillion diagnostic tests that took literally FOREVER, all to find that nothing was really wrong.
So I did a google search for my problem. Found some solutions. And everything is fixed. Bravo for me. I should have majored in Computer Science or something. LOL.