That's kinda odd. The CD drives Windows report are LITEON and LG, but the DOS drivers mentioned in config.sys is for an ASUS CD drive. What's the history of your machine? Did it use to have a different CD drive or something?
In any case, so far I'm unable to find DOS drivers on the web for either of the 2 CD drives Windows report for you machine. It's possible maybe they are new enough hardware that the vendors never actually wrote a DOS driver, in which case you wouldn't be able to use those drives in DOS.
As a test, try this: insert a data CD (not audio CD, data, meaning there are actual files on the CD) into either your E: or F: drive. Then run the command prompt in Windows (if you can't find it, go to Start Menu, select "Run..." and enter "command", without the quotes and click OK). In the command prompt, type the command "dir E:\" (without quotes, and change to F:\ if that's the drive you're testing) and press ENTER to execute the command. This attempts to list the files in the root directory of your data CD. I'm trying to test whether that works or not. I'm guessing it doesn't work, but I could be wrong.
[Exit the command prompt when you're done by entering the EXIT command]