there are companies out there that do this but usually for a prototype run - 10s to 100s of units. the set up fees are what will kill the quantity 1 run. Figure at least $1000 for 1. and dont forget, this presumes you got the schematic 100% correct - a somewhat tall order.
You are better off designing the board (or getting it designed - I raise my hand on that one...), having proto quantities of the PCB made and then stuffing it yourself (or hire some one to do that). Since you will likely have to debug it, I suggest you do stuff it yourself. and no, that wasn't a rude joke...