I'm trying to reclaim the metals on circuit boards and the vast majority is underneath the plastic coating. It is a brittle plastic that chips off in small flakes when etched but that process will lose to much of the precious metal.
This seems to be a popular question judging from some Google queries.
Printed circuit boards are made of a variety of materials, and from what I understand, the specifics may vary somewhat based on the specific needs of the product and the manufacturer. For example, in some cases, I know the PCBs are coated with special anti-static coatings to prevent delicate RAM and CPU chips from being damaged (e.g., this article found via Google among others).
So I doubt there's a definite solution - more likely you'll need to try several different things.
That said, there's a recent article that looks very interesting about separating parts by dissolving and swelling the plastic resins with DMSO: "Dissolution of Brominated Epoxy Resins by Dimethyl Sulfoxide To Separate Waste Printed Circuit Boards" Environ. Sci. Technol., 2013, 47 (6), pp 2654–2660.
Certainly DMSO is considered a near-universal solvent and will swell many polymers. So I'd probably try that first.
You might try Citristrip, which actually strips paint, but mine tipped over and spilled on a rather thick plastic packaging piece, and melted it over the course of a weekend. Benefit: Non-toxic.