A couple things to try:
1) Try the second drive as master and the original as slave
2) Remove the original and try the new one on the cable by itself
3) Try Schmoes suggestion of Cable Select for both drives
4) Make sure the new CDROM is getting power (test the eject button after powering on the PC)
Hopefully, these different configurations should give you enough information on what the problem might be. The new CDROM drive should definitely work on the cable by itself - otherwise there may be problems with the drive.
Definitely give us more info the next time you post. Let us know more about the problem, whether it shows up in the BIOS at bootup, or whether it's missing from both the BIOS and from Windows.
~cdogg
"The secret to creativity is knowing how to hide your sources."
- A. Einstein