|This video ......|
.....shows what appears to be a standard DVD drive behind the cosmetic door that flips open when the DVD drive ejects it's tray.
If you manually open the cosmetic door, there should be a tiny hole in the front of the drive itself, just below the front of the tray (I've never seen a standard drive that does not have that).
If you insert something stiff that's long enough such as a straightened paper clip that has a diameter not much smaller than the hole into that hole, push straight in, the tray should unlatch and pop out a bit. In this case, that may work better if you lay the computer on it's side so that the vertically mounted drive is horizontal and top side up.
Assuming the drive hasn't been damaged by someone hitting the tray from the side when it was open, and you haven't had a CD or DVD fly apart and possibly deposit pieces inside the drive, I've seen that sometimes a tray won't reliably eject because....
- it's slightly out of alignment in the case due to the way it's screws on either side fasten it to the interior of the case. If you loosen the screws on one side, shift the position of the drive a bit, tighten the screws, the tray will eject / retract reliably when you press the button for that on the front of the drive itself. You may need to try that several times - that may work on one side but not on the other side.
- or - at least one of the screws used to fasten it is a little too long, and that sometimes catches on something inside the drive preventing the tray from ejecting. Loosen the screws on both sides a bit, try ejecting / retracting the tray by pressing the button for that on the front of the drive itself to check for that.
If that allows the tray to eject / retract reliably, leave the screws loose (not recommended) , or better still, obtain shorter screws (screws that have a shorter threaded shaft) such as from a local place that repairs computers and use those, or use a tiny metal washer under the screw heads, or make a washer (spacer) from a thin piece of cardboard and use that under the screw heads.
For either solution, you have to open up the case.
In any case, the drive can be opened up if you remove it from the case and then remove it's cover to see what might be jamming it or is broken or loose inside of it, and standard replacement drives are relatively cheap to buy, especilly if you get a "bulk" drive (merely the drive in an anti-static bag). .