Confirm that they are both recognised in your BIOS, then try booting with
the WinMe Startup (floppy) Disk into Real Mode DOS, select CD-ROM support.
See if they are recognised. If so, note the temporary letters allocated to
each and use the DIR command to see if you can read contents of a CD in the
CD-ROM and the CD-RW :-

At the A:\> prompt type DIR X:  (where X is the letter allocated above and
note the colon after it!)

It should give a listing of the files on the CD and should help prove
whether its a failing drive or not.

Mart