http://etymonline.com/index.php?term=computer&allowed_in_fra...
The level of complication necessary is "can compute stuff". Whether you want to include any kind of functional transformation as a computation or not is up to you.
Example: Consider a hypothetical machine that implements standard SQL in hardware. Such a device would not be Turing-complete. Would you still call it a computer? I would.
EDIT: Thus a printer IS a computer, not for the procedural operations, but for that you can feed in some illegal input through the interface(no matter serial, peripheral or USB), and it will either send you back some complaint, or disconnect from you, or burn itself down.
On the other hand, this definition is very vague...