I have just encountered this issue with one of my customer today (08/14/2015) and the first fix i attempted worked. Therefore in this guide; i will only be listing the fix which has worked for me.
The issue was that after upgrading to Windows 10 from Windows 7 on a ASUS Mini PC – The DVD Drive was not showing up in My Computer and the Device Manager also did not indicate any unknown devices.
To fix the issue; i created a new registry key for the drive controller and then rebooted the PC. However, before you do the registry method; make sure you back up your registry settings.
see how to back up registry settings: https://support.microsoft.com/en-us/windows?ui=en-US&rs=en-001&ad=US
To continue; follow the steps below:
1. Hold windows key and press R
2. Type regedit in the run dialog and click OK
3. Navigate to the following path
4. Right click atapi and select “new” then choose new “key”
5. Type Controller0 and click OK or press Enter.
6. Now right click Controller0 and choose new dword (32-bit) value
7. Name the key as EnumDevice1 and click OK
8. Click EnumDevice1 and set value to 1.
9. Reboot your PC and TEST.