Slug is right on with checking cables/grounds. That PRNDL light runs through grounds etc from the trans. If those silly corroded cables didn't cause so many issues, Wren and I might be wrong on some of the diagnosis a little more often. As well..I'm not only the President of the Clean Your Connections Club...I'm also a member.

While we're still talking about cables and such, if you had to beat as much corrosion off of your battery cables as you made it sound, you might consider replacing them.

If the corrosion around the connectors and under the boots is that bad, it may very well have worked its way further down. Whiile your inspecting everything else, you can cut a slit in the insulation of the cables, and open it up just enough to take a peek. The electrical tape the crap out of it to keep from shorting out later if you keep the ones you have.