First and foremost, as you are probably aware, check the cable connection.
Does the DVD player have multiple output modes (composite, components, S-video, VGA or HDMI)? Which mode are you using? It is possible that the correct output is not set, so the video is not shown. For example, you connect the composite cable but set to component. Or, you connect a component cable, set to 1080p but the TV supports 720p only.
It is also possible that the DVD player is outputting an incompatible TV system, e.g. DVD player outputting NTSC while the TV only expects PAL. Most modern TVs (except those manufactured in the US, Japan, Korea and the like, many are for domestic use only and only support the TV system of their country only) are multi-system and can auto-switch between PAL/NTSC/SECAM, or provides a way for user to switch in the menu. But worth checking as well.