It depends a lot on the DVD player. CD players and DVD players use different-wavelength lasers to read the discs. The ones and zeroes on a CD are much bigger and farther apart on a CD, and so a longer-wavelength (and thus cheaper) laser can be used to read them. Most DVD players use only one laser to read all disks, and it's a shorter-wavelength one that is not tuned to work with the sizes of the ones and zeroes on CDs (there are some DVD players that have two lasers; one for CDs, and one for DVDs).
I've found that single-laser DVD players tend to be twitchy about what CD-Rs they want to read. Even different brands of CD-R media can affect the go/no-go state. Try (as Dave suggests) burning at a lower speed, and if that doesn't work, try a different brand of CD-R media (and still burn it at low speed; that can never hurt anything except your patience).
You might also try CD-RW media. The contrast between the ones and zeroes on a CD-RW is less than that on a CD-R, thus theoretically making it harder for a player to read, but you never know; your home player might hate CD-Rs but like CD-RWs. As an added bonus, it looks like CD-RWs have longer-term data retention rates (lower bit rot), compared to CD-Rs, so your burned discs will last longer and be editable. Bonus.
-BP
