Please make sure your Anti virus software and Internet Explorer do not run at the same time.

Does it mean when the Anti virus software is running, Internet Explorer must not be running and vice versa?

That's exactly what the sentence appears to mean -- but it doesn't make sense to me. Wouldn't you want anti-virus software running while on the Internet?
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I agree that it is not a good example. I'd like to use the word enable in the sentence and still to retain the meaning, does the following sentence give that?

Please make sure your anti-virus software and Internet Explorer are not enabled at the same time.
I think so, but you probably need a computer expert rather than a language expert.
Must be because of thorough-scan mode of the anti-virus software, and not in the background scan mode. So basically in the first mode don't run anything except for the anti-virus software.
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