Yes there are portable battery operated LCD televisions. Try the Haier HLT71 7-Inch Handheld LCD TV.

LCD TVs were initially meant for the portable market because they did not consume as much battery. The first commercially available LCD was made by Casio in 1983.

Most portable TVs have the option to run the machine on batteries, Modern portable televisions are LCD and thus able to run off batteries for quite a long time before they die.

It'll probably be cheaper to buy another portable player. Traditionally, the LCD screen would probably cost more than the original retail price of the player. Sorry, but I've replaced LCD screens in TV's still under warranty, where the LCD screen was 1-1/2 times the original cost of the TV.

Quite a few companies make LCD TVs with built in DVDs, but most of them are sized to be portable. Toshiba, Sanyo, and Haier all make well reviewed models.