Your best bet is to buy a cheap DVD player and put it in your own box and even that won't be easy since the electronics will be designed to suit the enclosure.
A PC-based solution might be a better option because the parts are more generic. You do know that you don't even need to have a keyboard, mouse, hard drive etc. You can buy TV output cards, remote controls etc. and easily put the motherboard and power supply in your own case. Mini motherboards are available for embedded applications if size is a problem. The trouble is this needs some experience of software and PC hardware.