If you go bak into 'Device manager' and click 'View' then 'Show hidden devices' does it show up ? If it does, click on the entry 'DVD/CD ROM drives', double click on the name of your drive and then select 'Drivers' from the gray pop-up box.
At the bottom of the 'Driver' page you will see 'Uninstall'. Click this and follow through a couple of warnings, accepting them, and delete the drivers. Then re-boot. Windows should automatically install fresh drivers for this device, and it should then show up and work.
If it doesn't, you may have corrupt driver files in which case run SFC /SCANNOW which will attempt to repair any faulty Windows files. To do this -
Press 'Win Key + X'. This will bring up a menu in which you should see 'Command (Administrator) and click on this. (It is possible you will only see 'Command' in which case RIGHT click on it and then select 'Run as administrator'). This will bring up a black screen with white text. type SFC /SCANNOW (note the space SFC and the /) then press 'Enter', then go and make yourself a coffee or pour a beer. It can take up to about 20 minutes to finish but do NOT interrupt it. When it is finished it will say if it fixed problems or not. Then re-boot and see if your missing drive shows up.
If it doesn't, post back.