Check your model to make sure there isn't a hole in the top and that all the materials on it are set to cast shadows. Then make sure you turned off the sun. :) (I love saying that) Aside from those two things - ummm not sure what else to suggest. Good luck:)

The model is intact (no holes), all materials are set to cast shadows, sun is off, but no change. The top of the lantern is made of a swept surface, would this possibly be the cause?

Looks to me like the fingers are not closed and the light is shining through the gap between the tips of the fingers and the wrist, showing in the thumb gap. Next, the lack of arm shadow on the wall is one of perspective. Draw a line from the light to the arm to the wall. Draw that in your mind (3d). If your wall is too far away, or the light between the arm and the wall in terms of orientation, you won't see a shadow. Also, make sure 'cast shadows' is enabled. By default it is so if you didn't make changes in your light object then you should be fine. Really, from what I see here, you have a wall way back in the distance, a light in the middle of the work area and an arm above the light but slightly closer to the camera than the light. This, to me, is a matter of depth of your objects. Hope this helps.

Ok, I looked closer, I see the perspective issue. You have the lantern directly below the hand. Thus the shadow of the arm will be on the ceiling. The hand is not closed, thus the light showing inside the hand where you don't want it. Also, the lantern is directly below the arm, which means no highlight shadow on the arm. Get used to it, Bryce is realistic and you have a realistic scene. If you want to change it, close the hand, move the lantern closer to the front (use a side view to see the perspective). Also, looks like you have the light too bright, turn down the intensity just a bit. As for no shadow on the top of the lantern, that's your sun control. Dump the sun. Give it black all the way around in the skylab. Change skies if you need to. I think they are interfering with the image. By the way, if you did put shadows where you want them, it would look wierd (but maybe that's what you want). Oh, if you turn down the lighting and shift the lantern slightly to the front, you'll pick up a shadow line around the lower part of the arm.

Thanks for all the ideas.I'm off to try them.