At a guess, the lines on the monitor were already a problem before watching the DVD, but you had not noticed them. The difference in contrast due to the black strip above the wide screen picture made them more obvious. Now, because you know that they are there, your brain highlights them every time you look at the screen (a bit like when you find a pimple on your face, you can't ignore it in the mirror).
Then again, it might be a new problem.
Most likely causes are either the input from the computer or the monitor itself.
If you can find a different input source, you can eliminate or confirm the computer as the cause.
I expect the other piece of information that the technical experts need to know is what type of monitor you have. There will be different potential problems for an old style cathode ray tube compared with a modern LCD flat screen.
Quack!
Geoff the Duck.