the fact that the device shows up on boot (in Bios?) is a good indication that the device is functional.
How did you know that the driver is running and up to date if you do not have the drive listed in your Device manager? I suppose you have installed an incorrect driver for your device. Also, please note that there is a difference between software for the drive and drivers for the drive.
If you have the model number and producer of your DVD drive, look it up on google in order to find and install the appropriate drivers.
The operating system comes with a built-in CD drives. uninstalling the current driver and reinstalling the os drive should fix the problem. Also there is a Microsoft fix it, solution available for this problem.