my desktop slot drive won't show disk on desktop and won't eject disk in slot.

Try setting up another admin user account to see if the same problem continues. Please post back on whether or not this worked. Also try the Safe Mode. Please post back on whether or not this worked.

Isolating an issue by using another user account

Safe Mode - About

If it works in the Safe Mode, try running this program when booted normally and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. Click “Share Report” button in the toolbar, select “Copy to Clipboard” and then paste into a reply. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information

That's pretty typical of an optical drive. Even the better models of those drives aren't particularly reliable, and having the internal optical drive replaced was a fairly normal occurrence with a Mac.

Is this particular optical drive an internal drive in a desktop, or an external drive attached to a desktop?

Here's a reasonable list of options for getting the optical media to eject:

Quick Tip: Eight Ways to Force Eject a Disc from Your Mac's Optical Drive | Other World Computing Blog

Failing that, it's probably then time for a repair.

Also check if there's still a disk in the drive. I've made that mistake on occasion.

You are welcome.