The first thing to do when you're having trouble with a disc is to test it out in another player; many modern computers have a DVD drive, and most gaming consoles offer DVD support. If your DVD is unable to work in any player, then issue is likely with your DVD and not with a single player.
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Your DVD may skip or refuse to play if it is scratched, cracked, dented or warped. Minor scratches are a fact of life for most DVDs, and sensitivity to these scratches varies between DVD players and models. You can purchase a repair kit to fix minor scratches at most major retailers; some movie stores can also buff out scratches for a fee. If the disc is otherwise damaged or too badly scratched, you will have to replace it.
If your DVD is only malfunctioning in one player, try another disc with that player to confirm the issue is with your DVD player/drive. DVD player malfunction can be caused by blown fuses, dust obscuring the laser lens, a malfunctioning laser or even simply old age.
There's a whole slew of reasons why a burnt disc might not work on your system: your DVD player may not recognize burnt DVDs at all, the disc may not have burnt properly, or you may have burnt the video in the wrong format. Burning at too high a speed may cause trouble during playback; try burning the DVD again at a lower speed if it does not work in any player.
DVDs have regions which help limit the distribution of a DVD to a certain area of the world or venue; likewise, most DVD players are limited to playing a certain region or regions. Unless you're using a region-free player or DVD, a mismatch in the region can cause the DVD not to play. You can check on the DVD box to see what region the disc is encoded for.
There are two video formats that you need to keep in mind: NTSC used in the Americas, and PAL used in Europe. These formats are not compatible -- you cannot watch a PAL disc on an NTSC DVD player. There are certain players that allow you to change the format; check your user manual to see if this is a setting available to you.