How do I open a Word backup document ending in .wbk?

Just Click the Microsoft Office Button, click Open, click All Files (*.*) in the Files of type box, locate and select the file, and then click Open.

And here is an article that might help you.
http://support.microsoft.com/kb/827099

That didn't work.  When you say click the Microsoft Office button, do you mean opening Word, then click open, identify all files, then find the file and click on it to open?  Please note that the .wbk backup file was probably created in Word 2007 or 2003, but I am attempting to open it in Word 2010 which is on my new computer.  The .wbk file was transferred from my old computer to the new one back in January.  Thanks.

Yeap this is what I meant. Open word then click on "Ms office button".  As i see you tried to open it in word and you get gibberish. Most probably that means it was created with word 2003 and you should try opening it with same version of office.

Another thing you could always try ..

* Backup your file first.
* Open word and Go to "File --> Open"
* As soon as the Open file dialog appears Choose your file.
* Next to "Open" button there is another button with arrow.
* Click the arrow and select "Open and repair"

Dont forget to backup your file first..

How do I backup the .wbk file when I can't even open it.  Should I just make a copy & put it somewhere else?

yes, just make a copy of the file. and follow instructions :)

Unfortunately, I get the same result when I try to access the file on my old computer where the document was originally created.  The version of Word on that computer is what it was created in.

Apparently, what I want to do can't be done in my situation.  Comments may assist others, however.