I found I had several computer DVD drives that wouldn’t work (tray stuck shut) and eventually found a fix. The fault is usually caused by a perished drivebelt, which is used to drive the tray in and out. Â The cure is to fit a new drivebelt. The repair is not hard if you are used to dismantling small mechanisms, but the most difficult bit of the job is sourcing a new belt. Â Getting an original belt will be almost impossible, so it resolves to finding one that is sufficiently similar to do the job.
Searching on the Web I discovered that this is actually quite a common fault, and is thought to be accelerated by ozone in the air.  Besides ordering a new belt online, correspondents suggest using rubber O-rings from a hardware store, rubber bands, and the neck ring from a toy balloon, all allegedly successful.  Each model of drive is likely to require a different size of belt (I found three sizes in those I opened, plus one which appeared to be gear driven. The belts were typically 1mm x 1mm square section, with  diameters of 20 to 40mm.)
I got one working and tested using a 40 pence O-ring from a hardware store, which was a lot cheaper than buying a new drive.