If it plays some dvds but not others then its probably the disks. Try cleaning the disks. (also make sure they are DVDs and not HD DVDs or blu rays.) Different play back software shouldn't matter unless you are talking about .avi's and not DVDs.
Check to see if the DVD's that play are all Single layer.
Some drives at the end of life(or defect) start to have problems seeing the second layer(done with red light[would guess it is an led] that lets it see the other layer, i have seem this "light" just stop working) on dual layer discs and will still play single layer just fine.
If a disk is under about 4.5 gigs its single layer up to about 8 or so will be dual layer so if ALL working discs are single layer, that may be the issue.
you know I never would of thought of that, I do believe you are correct about that though. just checked out the disk that played against the ones that didn't and you are right they do have that difference
If your laptop is used as more of a desktop, a external 5.25(Needs its own power) inch DVD drive will be faster(and in most cases quiet at dvd watching speeds) then another internal drive. Not a good option if you use it for portability however.
I say this as someone a slim laptop drive in my media center(they tend to be louder The Sony is my quietest(DVD/CD, loud for DATA) so far[laptop drive]. my Lite-on is louder. My LG external 5.25, nice and quiet ).