Help! Can my battery handle this kind of load?

I recently came across some 5.6" monitors made by Rosen, the only catch is the are made to attach to the back of a PS One, sort of a game console and screen for those on the move. Here is the catch, the are made to run off of 110v using a power adapter that comes with the PS One, power input is rated @ 7.5 volts the adapter says it is 2000mA it is desinged to power both the screen and console " the screen mounts onto the back of the console" I adapted the screen to mount in my headrests after removing them from their original housing. I found a adapter made by Sony for this specific purpouse, it has a ciggarette lighter adapter on the end of it. found a trick to wire the adapter to a relay instead of plugging into the lighter socket, i have to monitors in the headrests plus a dvd player and Playstation one the dvd and playstation are never on at the same time. How do I know if I can Run the two monitors and either the dvd or playstation at the same time? Each has it"s own seperate inverter. Thanks day952

Enuro! Its a 1997 honda accord, there is a alpine cva 1005, and a small sound stream amp also running off of the vehicle. what i meant was there is a seperate inverter for each device ie: two monitors in the headrests and dvd player under the seat= three devices= three inverters. the lcds are meant to use 110v current but are sold with a inverter that makes them able to be used in the car " cigarette lighter adapter" thae screens were only $35 because they were on sale so i figured i would give em a try. thanks for your help.day952