Video drivers shouldn't affect DVD playback, or at least I don't think so.

Are you sure that the DVD is fine and that the drive is fine too?

If they both are, I dunno, what error comes up? or what seems to occur?

As for finding the videocard,

1)right click on my computers
2)go to properties
3)go to hardware tab
4)click device manager
5)expand display adapters

Or there are GPU tweaking programs that will tell you what you have, but you'll need to know whether your card is ATI or Nvidia first. I guess you can search through add&remove programs too alternatively and see what kind of drivers you have