I'd say no it isn't illegal - They own the music, and they are paying you to put their music onto a DVD slide show. You're charging for the service or making the DVD, not the music itself.
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I disagree. They own the CD the music is on, not the rights to the music itself. The CD sleeve will have a paragraph prohibiting unathorised "distribution, reproduction" yadda, yadda.
By ripping the music files and inserting them onto the DVD, the OP would be reproducing the music.
The fact that he's also intending to do this for profit makes it 100 times worse.
An analogy would be a movie you see at the cinema. If the Director uses a piece of music, he must pay royalties to the artist. Usually the artist will also insist on a listing in the credits too. The OP's intention is essentially the same - whilst the audience is of course much, much smaller.
As Pat says, you need to find some royalty-free music. Either that or find some local musicians / bands who will let you use their music cheap/for free. You'll be supporting local talent and they'd probably appreciate the publicity.
The other alternative is to look into how much it would cost to pay royalties for music. I don't know how much this would cost, or how easy it is. I know that pubs, etc, can buy CDs of music with the royalties pre-paid, but I don't know if they are allowed to be used in recorded media or only to be broadcast directly.