Try physically removing both drives' rear IDE connections first. Shut down your system.
Then reattach the DVD-ROM's connector and switch on, allowing Windows to install new hardware and its basic CDROM driver for the drive (should come up as D).
Again shut down the system. Reattach the rewriter's connections and Windows should again install new hardware and the CDROM driver. This time the drive letter should be E (assuming you have no other peripherals).
If this doesn't work then the most likely reason is a loose connection elsewhere, probably at the motherboard where the IDE cable is attached.
If the drives are not currently listed in Device Manager but are when in Safe Mode, then it is almost certainly a loose connection(s).