Button wise you can bypass it -- there is a reason those old flashing tools had a little button that could eject it. You had to bridge a couple of pins on the power supply cable but I can't remember which offhand.
What is more likely for an original style 360 (slims tend to be someone ripped the ribbon on the faceplate) is dust and a worn belt
https://www.instructables.com/How-to-Fix-a-Stuck-Xbox-360-or-PC-Disc-Tray/
https://www.ifixit.com/Guide/How+to+easily+fix+a+Xbox+360+drive+that+wont+open./111352
also presumably why the poster above saw one magically spring back to life -- get the right location, humidity in the air, persistence, heat... such that it gets enough friction and yeah. Such things however will return, and maybe with a disc read error aka DRE in some circles.
I have seen people break the eject buttons before but that is rare and usually done when someone has pulled it apart to mod the thing or had the 360 try to learn to fly.