I assume when you say both are working properly, that means you can read data off of disks from within your OS, correct? Those lights blinking only means they have power, which is still good to know.
Here's something you can try. Restart your computer and press F12. What F12 should bring up is a one-time boot menu (this seems to be standard on Dell computers). From this boot menu, see if the computer will boot from the CD drive (or if it gives you other options like your DVD drive).
Did you try editing the boot-order, what other devices does it let you select from? Did both drives (CD and DVD) come with the computer, or did you add one in later (Dell has so many configurations)? It's possible the computer is confused. Are both drives SATA or are they IDE, and if they're IDE, are they on the same cable? If they are IDE on the same cable, try booting from whichever drive is master (either set by jumper and/or at the end of the cable). If you added-in a drive, remove it (or if both drives are on one cable, remove the slave drive).
You could also try resetting the BIOS (unplug the computer and remove the battery for a minute), then go back in and reset the boot order, see if that fixes anything.
Otherwise, I'm not sure what the problem could be besides something broken in the computer.
Try removing the CD drive from the setup, leave in the DVD drive. Set it as Master. Make sure the data cable and the power cable are properly plugged in the drive and in the mobo. Reboot and see what happens when you do the F12.
If it doesn't work, do the same but with the CD drive instead of DVD drive.
If none of the above work try updating your bios to latest version, via dell website.
To be honest though to be one of the settings just set wrong, as House70 said check its all set as master and all connected ok, if not try rotating the connection on both cd and dvd drive with each other.