The Pin Oak, that my late father grew from an acorn, looks dead, AFAICT.

He had it in a very big clay pot, which was also filed with various bulbs
such as Daffs. They flourished ... the tree died. It was about 4ft high.

First I want to be sure. What is a 100% method of telling if a tree really
is dead, or if it's just sick or dormant?

I pruned off a thick lower branch, and there was no sap at all; it was
completely dry.

I picked up the pot, which simply crumbled away in my hands, so I smashed
the pot and removed the tree. Looking at the roots, they were not very
extensive, but looked OK to me. There was no evidence of grubs, and other
than the lichen, no disease either AFAICT. I then replanted the tree in a
mix of compost and bonemeal, straight into a deep hole about 4'x4' in the
middle of our front lawn; ever hopeful, and gave it a good drink.

There's been no leaves for two years, and it's covered in green
fungus/lichen. When I cut off the branch and examined it, there were lots
of little mites of some kind, that looked like tiny flies. To cap it all,
there was a big cobweb round the top ... like it was trying to tell me
something. It seems obvious to me that it's dead, but could I be wrong?

If it is dead, I want to replace it with another Pin Oak which,
ironically, I hear thrives in the type of soil we have round here (sandy,
clay). This time I want to be sure I don't kill it off, although the main
reason for the other one dying was probably just neglect. It probably died
of dehydration, since I never watered it (figuring it's OK if it's
outdoors - doh!). I've only recently taken an interest in gardening.

Any links to web resources or ye old fashioned books on the subject of
tree care (with any specifics for Oaks), appreciated.

TIA,

-
[H]omer