Totally mute CD player

It's possible the drive is broken.
Just for starters let's go over the basics.

Did the disks play before now ?

Do the disks play on the normal stereo ?

Does the drive access normal computer data disks OK ?

The disk is in the drive the right way up, label on the top ? I know someone who had a problem where another person who shall remain nameless told them that computers need the disks label down. Duh !

The disks are clean ? I mean clean not just shiny.

When you put a disk in can you hear it spinning up or do you just get a steady sound ?

When the disk is in can you get at it via Windows Explorer and not just the media player ?

If the drive isn't accessing data disks or playing music then I reckon it's toast. It might need cleaning or it night need replacing. Cheaper to clean it first with a proper CD lens cleaner. Don't get in there with the MR Sheen ! ;-)
If you do have to replace it, don't panic as they're very cheap and very easy to change out.

Totally mute CD player
Problem solved - or at least sound now available. The volume control icons had disappeared from the bottom of the screen and from the desktop - why I guess I'll never know. So thank you, Heliotrope for your quick and comprehensive checklist. I went down it, and answered positively to every question, so I suddenly thought of the volume control, and began to wonder where it went. Now I have it back, and all is well.

Funny thing, though - my lovely Great Pianists of the 10th Century doesn't get recognized as such by Windows Media Player. It just gets listed as "Unknown Artist"! But it plays, so that's fine.

The titles can be entered & uploaded to the online database it's using so that they'll show for others automatically in the future.

Totally mute
Thanks, Monger, for the suggestion. but how does one do that? Is it complicated?

MusicMatch Jukebox has very comprehensive facilities for uploading the titles and downloading or changing them also.

What these programs are accessing is the CDDB, CD database.
Run a google for it or check www.cddb.com