I made a design (using Adobe Illustrator) and I want to print it onto
11 x 11 x 2.5 inch box.  I need to make only ONE professional
prototype so I am looking for a company that does it?

More difficult (costly) to print onto the box itself, but any
signwriter with a large format inkjet printer could do photorealistic
prints onto sticky-back plastic, which can be applied to the box.
Suitable for a prototype.

Owain

I have finished making a boardgame and I want to take a picture of
people playing the game, which will go on the back of the box.  Since
I need that picture before I send it to production, I need a
professional box as if just came off the production line.

The whole challenge is taking a realistic picture of people playing a
game that doesn't exist.

The only site I found so far is http://www.mjscreations.com/game.htm 
but they charge over $250.00 so I'm looking for an alternative since
the price is a little steep.

from what a remember about boardgame, the picture is printed on a
piece of paper first and next put on the box, not printed on the box.
look at one you'll see