Yes, likely illegal, yet very low risk as no one else is damaged, few will know, and you can easily stop if challenged. As an IP attorney, I want to advise you to respect copyright and not do this. Would you want this done to your copyright protected material?
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I take it you mean that the copyright is owned by someone else and that you haven't received permission to copy the image.
The answer to your question is probably YES, subject to the qualifications expressed by Attorney Burdick.
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I respectfully disagree with my colleagues-- I think since the use here is only on your personal computer only, it's highly unlikely that this would be considered copyright infringement. If you were displaying it in public for a profit it would be different.
As a practical matter, using a copyrighted image as your background screen on your personal computer is not going to get you in trouble with the copyright holder. While it doesn't constitute "fair use" in the affirmative defense sense, personal, non-commercial use of a digital image for your screen saver is akin to decorating your room with cutout images from magazines. Theoretically, if the image is being sold as a screen saver, and you somehow managed to get your hands on a copy without paying for it, the copyright holder could assert a claim against you, but it's highly unlikely.
Yes it is illegal, and more importantly to you, it is actionable. I have seen a number of clients get demand letters out of the blue for using copyrighted images on their website (most of my clients swear they did not know the image was copyrighted, but that is irrelevant).
You should take down the offending image, to prevent an unnecessary legal headache, and expense as there are statutory penalties and fines that can be imposed even if there are no actual damages.