A good stiff brush might bring the boards back to life, I will bet that rust is not the only problem. Tin Whiskers.

Gotta make you wonder -- maybe the long debated claim of electrical rust prevention isn't all that 'hocus-pocus' after all...
Should not be a debate when it is basic chemistry, or electro chemistry.

It is not so much from forcing a current through to prevent corrosion as it is more of giving the charge between dissimilar metal a path to flow to.

Look up underground piping. Here in the US it is even in the building codes for gas stations as an example. The steel piping is required to be grounded in certain places with an anode in other places. The layout of the job determines the placement.

The same applies to water tanks if they are not lined with a coating of some sort or a bladder.

So when you power a board a path is created from the positive potential to the negative potential.

The example skimask gave shows how a forcing of current effects things, more along the line of electroplating, ( in his case as he said, he is not plating ) but it is still working on the theory of ionic exchange. I say theory because we currently use stuff from Dalton, but we may find that Keely is also correct. There is something to debate