I fixed a Bose 321 system with a stuck DVD drawer. Once you open the case you will see that the DVD unit looks to be a standard DVD unit you would place into a computer and could likely be replaced with a cheap one from your computer store if you are unable to repair it.
The root cause in my case was the small white gear attached to motor drive shaft. It had slid upwards so that it didn't fully mesh with the mating gear and in addition it was blocking the opening of the drawer itself.
That causes a problem in that you need to open the drawer about a half an inch at least in order to be able to snap off the front faceplate attached to the drawer. The faceplate has snaps on the bottom and slides upwards to remove.
Once the drive drawer faceplate is removed, the drive itself can be removed from the unit and you can gain access to the drawer eject pin hole that is present on most (all??) computer type DVD/CD units. This small hole is present on the lower right hand side of the front of the unit. If you stick a straightened paper clip into this hole and push, it will cause the drawer to eject.
I was able to do that to get the drawer open at which point I could see the small white gear on the motor drive shaft. I pushed the gear back onto the drive shaft properly and put a small dollop of epoxy on it to prevent it from moving again. After doing that the drawer opened and closed perfectly.