looks like you are going to need to make a seperate power supply for this screen.
i think a couple maxim chips and their associated circuits should be able to put out the power that you need for this thing.
a max787 will give you regulated 5V at up to 5A
a max1771 will give you regulated 12V at up to 2A
both the datasheets from www.maximic.com will give you a typical circuit design, that should be enough to slap something together to put out the power requirments of the screen in a 12V environment.
the 100% margin on the current capabilites should cover any spikes you might see...
wait a minute.... are there 2 power supplies for this screen????
now im confused. i believe there is only one power jack on the casing, so only one voltage should be required for the screen to run.
anyway, those maxim chips should be enough to get started on the supply, if you need more current on the 12v for some reason, then put an identical 12v circuit in parallel and have a common input, output, and ground. that will double the available current on the output.