Mac Pro cd drive stuck open

You have a couple options, depending on how stuck it is....

Tap the Hinges

I had this problem, too. I was able to fix the problem by pushing on the hinges, as shown below. In the image, you can see the cover hidden behind the outer "mesh" of the case, below the CD tray opening. It is supposed to snap back up from there when the CD tray hits those little hinges. Sometimes it gets gummed up, and it just needs to be nudged a bit to snap back up.

Open and Clean the Case

If you are unable to nudge it out of place, it's likely really stuck. You'd probably want to remove it from the case and examine it. It might need cleaning: either blowing dust away with compressed air or gentle scrubbing with a toothbrush. If it's oily or sticky, you might want to use a tiny bit of warm water, even less soap, and scrub gently with a toothbrush or paper towel (let it dry completely before connecting it to power!). You might find that the spring mechanism is broken or missing, in which case you'd need to replace those parts.

Professional Help!

If you are unable to fix it, you can bring it your local Apple Store or authorized retail/repair center and see if they can fix it.

It's likely the case will have to be replaced. I've fixed this before by lightly tapping on the area below the gate, but it's a recurring thing.

You can also slide the optical drive housing out and take a look at the mechanism that raises and lowers the gate. Try manually pulling it up and down a few times.

I got it fixed by inserting a needle in the case’s holes right underneath the lid. Keep pushing it up while holding the lid with a slight press, repeat the process and keep switching the holes all the way up!

EDIT: I made a quick video tutorial for easier explanation. https://youtu.be/PWO96pk1gOs