Nope. That actually makes the picture worse, albeit in different ways. And no, the computer can’t play DVDs.
I’m thinking the tech guys in the shop are probably correct.
Update: We just purchased season #4 of Futurama from a different shop, and it looks perfect. Inspecting the actual discs themselves, you can see light through the previous ones with a problem if you hold it up, so I guess disc quality was the answer after all.