I'm not familiar with the Cybershot or its software. If you can transfer the photos from the camera onto the hard drive, you should be able to use any burning software to save then to a blank CD as JPEGs.
Try Nero or
DeepBurner. If neither of them recognise your CD-R then try this method... it's usually for when you can't see the drive at all in Windows Explorer, but it might help in this case and won't do any harm even if it doesn't work.
Go to Start > Run and type
regedit
Important: Make a backup (export) before making any changes to the registry
Remove the
Upperfilters and
Lowerfilters values from this registry key:
HKEY_LOCAL_MACHINE \ SYSTEM \ CurrentControlSet \ Control \ Class \ {4D36E965-E325-11CE-BFC1-08002BE10318}
Then reboot and see if your CD drive is recognised.