The DC-D2831 and the DC-D2930 are very similar models. The problem of the disc draw not opening is often caused by the disc draw being stiff in its travel, compounded by a stretched disc draw loading belt.
The problem is also compounded by cold temperatures making the problem more noticeable during the winter months. The turntable can be removed by the removal of the top side screws and then unplugging of the motor/audio plug. This will give you access to some of your discs. The cure is more involved and if you feel this is outside you field of expertise then it is advisable to take the unit to be looked at by a serviceman (that's if you can find one in this day and age). However if you are feeling self confident then continue.
Remove the two side panels. Remove the two ribbon cable plugs either side of the cd mechanism.
The cd mechanism is fixed to the baseboard by several screws on the bottom of the unit, remove these taking note of which screw goes where. Remove the two screws holding the front of unit to the base board. Carefully ease the front section forward along with the cd mechanism as far as existing cables will permit. The release gear for the disc draw is on the underside and towards the front of the cd mechanism .
Rotating this gear will open the disc draw and you can now remove the disc draw front trim (this is clipped in place and is a real pain to remove). You can now lift the front unit out enough to remove the cd mechanism. Remove the disc draw loading belt and slide the disc draw out manually. Clean the disc draw runners and the laser assembly lifting plates. A thin application of a suitable grease will help. Having done this slide the disc draw in and out manually, feeling for a smooth action with no binding or sticking of the draw. Do not slide the disc tray fully in or it will lock into position and you will have to rotate the draw release gear again to open it. When satisfied that the draw has free and easy movement then replace the loading belt with a new belt. Reassemble the unit in reverse order but do not refit the turntable or the disc draw front trim at this stage.
Plug the unit in and observe the action of the cd mechanism, the turntable will rotate and unit checks for presence of discs. Press the disc draw open button, dose the draw open smoothly if so then unplug the power cord to the unit while the disc draw is in the open position and refit the front disc door trim. Refit the turntable and check all the functions of the unit. If all is good then give yourself a pat on the back for a job well done.
best regards from Vintie