How can I recover QuickTime movies from old CD's?

There's no magic that will fix faulty hardware.

Try them on another computer or try a different optical drive.

The OP says that they can still open some stuff in QuickTime - which implies that the Mac is reading at least some of the discs.

That said, a Mac might reject old discs for reasons other than faulty hardware, or defective discs.

If I remember other threads in this forum correctly,

• Apple removed all support for the HFS (no "+") filesystem in Catalina.
• Versions of macOS since then will refuse to read CDs formatted using the HFS filesystem.
• In the old days, there was the option to format a CD using two filesystems, so it would be readable both on Macs and on PCs. Although recent versions of macOS could read the "PC" filesystem, when they see that the HFS one is present, they refuse to read the disc at all.
• This leads to the conclusion that old "hybrid" Mac CDs might be readable on Windows PCs – but not on modern Macs!

DVDs have a standard filesystem (UDF) meant for use on DVD-Video, DVD-Audio, and DVD-ROM discs. Therefore, it seems more likely that you'd run into this problem with old CDs, than with old DVDs.

Sounds to me like it was reading disks and is now rejecting everything.

If that's not the case, I agree with your reasoning as to why it may be rejecting disks.

Unfortunately, the OP really hasn't provided enough information to be able to troubleshoot effectively.

Your question isn't really clear.

Are the disks unreadable?

Are you getting errors trying to read some or all of the files on the disks?

Please explain what's wrong.