here's some news for you: every new PSone LCD screen comes with it's own power cord.
why? you might ask, since it hooks onto the PSone and they both share one power cord. well the answer is because you can use the PSone LCD not just for the PSone (it can be used as a monitor for DV camcorders and other video equipment that uses mini-AV plugs) and those people would need a way to power it up if you bought it for this purpose and never owned a PSone system itself.
so, if you buy a PSone LCD screen by itself, you'll have no problem getting it powered.
and yes, they use the same power cord. if you buy a PSone system and a PSone LCD seperatly, you will now own two power cords, one to use and one for extra.