Although I've searched some for info on newer kinds of monitors, I haven't found much useful info on life and/or modes of failure. The symptoms vaguely described do sound like a monitor defect.
We will infer, from your third or fourth post that you are talking about viewing a DVD movie on your computer and aren't talking about a DVD player and separate monitor(?).
You still haven't told us whether you are using a flat screen or a CRT monitor, or given us a monitor model/maker identification (which should be imprinted on the front of the monitor). The failure mode described makes best sense for a flat screen monitor(?), although there are similar effects sometimes seen in CRT types.
A fairly remote possibility is that the program you use to play DVDs, or the DVD itself, may have ordered a change in graphics drivers, and failed to restore your usual driver when the movie was over. You haven't told us what OS you use, but for most recent Windows versions you can go to the Hardware Manager/Device Manager and delete the driver(s) for the graphics display/monitor and reboot. Windows will find and reinstall an "appropriate" driver when the computer restarts. If your monitor came with an installation disk, you can also follow the instructions on the disk to reinstall/change the driver.
In addition to the monitor, your computer must also have some kind of "graphics card" in order for the monitor to operate. A graphics card failure could possibly be a source of the symptoms described. (I've replaced three in my current machines, since the newer ones that one can still get all run at very high power levels and tend to cook themselves to failure.) You may have an "integral graphics" setup, with the graphics components on your motherboard, in which case any setup software would be on your original system disks.
Most "add-on" graphics cards should come with at least some kind of limited diagnostic and setup program. You may have a diagnostic/setup program on your computer that will allow you to display "test screens" that would show whether your "screen defects" are part of the screen or are coming from elsewhere.
Your comment that the off switch doesn't work implies that this is a fairly old monitor, and that it's been on most of the time (unless you've turned on "green" controls?). I haven't found much on wearout rates for flat panel monitors, but would expect anything more than three or four years old to be "suspect" for old-age behaviour. If yours is a couple of years old, and has been more or less constantly on, add another point in favor of a new monitor.
Last resort (or first if you really want accurate answers) is to find the website of the monitor builder and see if they have information and/or updated drivers that will help you figure out what to do next.