Is FCC-accredited testing required again if circuit board is placed in a different package?
I am going through this too, and likely late for the original question, but thought I'd share.  FCC requirements are for anything marketed or sold that emits electromagnetic radiation.  If it's a computer or gear that isn't supposed to transmit then it is, as mentioned, an "unintentional radiator"--so it's now in that ballpark of rules.  If the device is for commercial use, not in homes, then it falls under the Class A rules (less stringent).  If it is for residential use you have to follow the rules for Class B.  If you are encasing the whole product inside something else then you don't have to go through FCC validation and can use the existing approval.  If it is a Class B device with an FCC statement on its label then you can put that same info on the outside of your box.  If you don't want to use the full product and put parts in your own resin case then you have to go through the FCC processes.  If you market and sell and then get caught you could end up with severe penalties, along with being stopped from marketing your product.

Start at:
http://transition.fcc.gov/oet/ea
Note the "Application Information" and "Equipment Authorization Procedures," including:

Verification
Declaration of Conformity (DOC)
Certification


To get an idea of testing go to this page:
http://transition.fcc.gov/oet/ea/fccid/ and plug in the FCC ID from any product you have handy that has an FCC ID (or you search the Web for one) and then you can see the report that was generated--including a description of the lab setup, the tests, and the report data.

We will work with a lab for the testing but also work on our own testing ability so that we can do at least part of it on our own (so that we don't go to a lab with something that won't pass).

Good luck.