DIAGNOSIS Yeah, this one's common. It's almost always a power or setup step you've missed, not a dead unit right out of the box.
FIX First, check the obvious: is the power cord fully plugged into the back of the unit *and* into a live outlet? The plug can feel seated when it's not. Next, the unit has a physical power switch on the back or side—make sure it's flipped to "I" or "On." Finally, and this is the key one for these portable ice makers, you have to add water *first*, above the minimum fill line inside the tank, before any lights or functions will activate. The machine won't even power up for a dry run.
IF THAT DIDN'T WORK Try a different wall outlet with nothing else plugged into it. If there's still absolutely no sign of life, the internal fuse might have blown during shipping. You'd need to contact customer support about that.
HEADS UP Don't keep trying to power it on without enough water in the reservoir; the pump can get damaged running dry.