Region 0 should (in theory) play on any drive. (BTW, if this was a "normal" TV show or "proper" film the R0 suggests that it is likely, but not necessarily - "Mortal Kombat: Conquest" was released region free - a bootleg; you may want to consider trying for a refund).
I guess that it is possible that either the region labelling is incorrect (eg it is something other than R0 or R2) but would still expect you to see a region code warning in that case. If you know someone who has a disc from another region you could test that theory, but (especially if you do have an iffy copy) it could well be that it is improperly mastered and that your laptop is being more picky than your standard machine.
Intervideo WinDVD is a DVD player that often comes pre-installed by computer manufacturers. You could try VLC or KMPlayer (both free) instead.