I've successfully opened the case and re-attached the ribbon cable and now have a working dvd player (DRC630-N).
Once the screws are removed, you will want focus on separating the case at two clip locations on the bottom of the player, centered approximately 1 1/4 inches to either side of the brass threaded insert on the bottom.
You can see one of them broke for me when I was trying to get it open. If you apply some pressure under those clips you may have more success avoiding any clip breaking. I'm not worried about it since with all the screws it is plenty secure. What I did to get it open at these clips was insert a small flat screwdriver head in the small gap (seam) at the clip locations and twist. It did gouge the plastic a bit, but worked well enough. Once this side opens up you should be careful about separating the unit along the side with all the plugs. It took a bit of easing around the volume wheel and a couple plugs to get it fully apart. The opposite end of the player from the clips will come apart once the clips have been released as it is on a separable hinge.
Here is the ribbon cable detached from the circuit board.
The ribbon cable (blue part) slides into the black and white connector. Make sure the black part is pulled slightly away from the white part when you are sliding in the cable. Once the cable is in as far as it will go then slide the black part of the connector until it is flush against the white part. This secures the ribbon cable in place.
Here is a picture with the ribbon cable slid all the way into the connector and but still unsecured:
Now here is a picture with the black part pushed tight with the white part of the connector:
Here is how it looked when I closed the case back up:
Good luck. Hopefully this helps.