Did ya try something like this:
Press and hold the reset button on the front of the CD player. This button is often a small black indentation that must be pressed with a pen or a pin, and will reset the settings and force eject the disc.

 

There are no reset buttons on radio unit for a 2013 Avalon Limited with Navigation screen.

 

For the majority of Avalons, you can restart the operating system in the head unit by pressing and holding the on/off knob (that's the same knob that serves as the volume knob). My deceased 2013 Avalon and my 2018 Avalon both reset in this manner. They both use a different head unit than yours. (You do have the factory unit, don't you?)

Another method that may work for resetting the head unit is to disconnect the battery for a few minutes (5-10 minutes?). While the battery is disconnected, press various buttons on the head unit to help dissipate any latent energy stored in the unit's circuit boards. You will possibly lose some customizations (presets, contact list, saved locations etc.) in your head unit after doing this. Additionally, the car may drive funny for 20-30 miles because the ECU may need to relearn your driving style.

These are general things to try. They is not a guarantee that they will work, but the cost to do them is $0. I was not able to locate a copy on Toyota's owners site that was specifically for the HDD Nav unit. I'd suggest going through the settings menu and looking for a reset option. If you find one, do it. Also, if you have a copy of the HDD Nav unit owner's manual, read it. It may offer a suggestion.

 

Thanks, I tried all the manuals, nothing there. The thing is it is trying to eject, which leads me to believe it is a purely mechanical issue.

 

It doesn't have one of these?
pg 117 OM.

 

I know the 2013 and the 2014. Avalon Limited"s have different CD Players They have the fold down Nav screen for the disc insert. The 2015 Limiteds started having just the slot above the radio. With the Nav Screen down there is a icon on the glass for eject disc. Try holding down that icon to start the eject. The other option would be to press and hold the close button on the dash at the top right corner and a gentle push or pull on the folded down Nav screen to try and get it to close. I would also try the battery disconnect first.

 

Take your car to a good audio repair shop. They are your best shot at getting this resolved. They know all the tricks and techniques for this kind of thing.

 

Problem Solved!! Really nothing to do with the radio unit. Local library added a sticker to top of the first and last CD of all new books they get. This is in place of the old style RFID's. This made the disc too thick to eject. With a friend's help we got the cd out of the radio without disassembling anything. I will never put one of those new CDs in my radio again.

 

Want to tell us the trick? What worked, because none of the other ones has yet.
(I haven't tried the battery disconnect, but mine is stuck because the CD manufacturing company made the art work on the CD too thick, and I didn't get the warning in time.)