I have two very long MS Word documents.  Each is a version of the same
chapter in a book I am writing.  One version has a more recent
revision of the text, while the other version has had the endnotes
edited to reflect the correct citations.  I want to copy the endnotes
from that version and paste them into the other document, overwriting
its badly formated endnotes.  I am using MS Word 2003, and I also have
Open Office 2.0 available, and if necessary I can reinstall Word 2000
or even Word 97.

So far, I have tried selecting all the endnotes by right-clicking on
one and then using "select text with similar formatting" from the
context menu.  I then copy them, and select the endnotes in the
destination document using the same method.  When I paste in the new
endnotes, it either crashes the computer, or takes several minutes to
give me a list of about 400 blank endnotes.

You are understanding that in your first document, call it the rough
draft, when you inserted foot notes MS Word did some work under the
covers that you don't see. It is creating links, so that when you
re-read your work and add in end notes or foot notes, it re-numbers
them for you etc. So there is linking going on.

I am not sure I understand completely whether you mad a Save As or how
you started your second document. Because of the linking going on you
will not be able to en mass just copy and past. You can still
accomplish what you want to do, by going to the rough draft version
which has the good citations, and copying each citation one by one
over into your revised document. You sut already have inserted the End
Note into the main body of your document, either by when you did a
Save As to create the second copy or else by manually inserting an end
note in your second document.

If the text is good but you just don't like the the formatting of the
end note (i ii iii verses 1,2,3) you can change that by going to the
end note, highlighting it,
Menu Bar\Insert\Reference\Footnote\ Chagne the format to what you
like\and leave the Apply Changes To as is displayed "Selected Text"
then click ont he Apply Button.

Depending on what you would like to do I hope I have given you
guidence on both problems you are having.

One individual tidied up the citations for me, while I continued to
work on the text. The placement of the endnotes within the text,
meaning the words they come after, and their number and sequence, is
the same in both documents.  What was edited were numerous graphs and
charts, as well as some text not related to the things I am citing.  I
want to take just the text of the endnotes and transfer it. 
Unfortunately, there are far too many to make it practical to do
manually, so I need a way to copy and paste just the endnotes.

To clarify your second question, these are already endnotes, inserted
using the Reference, Footnotes function of Word.