There isn't much to go by, but a DVD player is a quite simple device. I think it to be one of three things:
1. Bad cord or power connection. If the cord detaches from the player, make sure there is no debris inside the cord or player. If you can, use a multi meter to test continuity. Also, make sure that outlet is good by plugging other devices into it.
2. Electric problems. The player may have been exposed to static electricity, which could have ruined it. Or, the player was not on a surge protector during a surge. Alternatively, the voltage for the player may be different from what you have in your house. Either 120v or 240v.
3. Power button is broken, which will happen after too much wear and use. If this occurs, it should power on by pressing eject or using the button on the remote.
Hope this helps!