Dave,
Sometime ago I had a HP 3457a that would take off and do very weird stuff, error messages. All of the power supplies dropping about 50%. Sometimes a light smell of electrical burning. Turned out to be the 120/220 AC line switch . The 3457a is in very good nic , must have sat somewhere for most of its life.
I have never seen contacts so black from corrosion. If You get back to that scope, Give it a shot. Also that scope is known for bad board to board connections.