Chicks are fragile, and death in the first days is not uncommon (I've had very good luck, but I know many dont). Cold, disease, stress from being shipped, super doses of all sorts of meds, birth defects... All you can do is make sure there's clean water and food available, and adequate heat...
That is not an unusual position for chicks to sleep (I know it looks scary, but they just plop down like that). What would be of concern is the lethargy. If she's eating and drinking, she's probably fine!