Cannot import Microsoft Outlook contacts

What version of Outlook were you running on the old pc?
Two options.  Return the old hard drive into the old pc, start outlook on it, right click on the top level on the left and select properties to view the location of the PST
OR
Probably easier, search the entire E drive for .pst files.  Unless you deliberately named your data file something else, it's most likely called Outlook.pst, but I'd search for *.PST and see what comes up.
Once you find the file, OPEN it in Outlook.  Then select all contacts and copy them to the new PST file.
This assumes that your contacts were stored in a PST file in the first place and not only on Exchange or in the windows address book.  If either of these are the case, please let me know.
 
Hope this helps.

Ok  First of all the old computer died.    I found .PST files.  Ok  I will "Open" the files under "File" "Open".   I have to ask the owner if the contacts were in Microsoft Outllook contacts

OK, so forget the "put the disk in the old" pc idea.  If you have the PST files, you can File->Open all of them.   You'll then see if there are any contacts.
If, for some reason, the owner had the contacts in the windows address book, search for .WAB files on the e drive.  Let me know if that's the case and I'll see about converting those to a PST.

Can you find a backup.pst file?

I have an identical computer that I was able to boot the old drive to.   Under "Contacts" properties it says the contacts "Location:  \\Personal Folders".  BUt I cannot find that.  I opened all >PST files with no luck for the contacts.   Any ideas?

Can I export the contacts to a regular file on a flash drive off the old drive in Outlook?   Then import them on the new drive?

That's not really necessary.  You can open the original PST and the new one at the same time.  Then just drag and drop the contacts from the original pST to the new one.  
Much easier than exporting and importing.

I found the back up file and copied it to the "Outlook" folder under C:\\local Settings\Application Data\Microsoft.    When I open outlook the inbox opens and I can see the old e-mails.   When I click on "Contacts" on the lower left side, I see the contacts.   BUt when I try to open the address book, I get an error message saying the contacts folder has been moved or deleted.  How do I direct the address book to open the contacts that are showing so I can use the address book for E-mails?

Oh, sorry, I missed your 2nd to last post above.
 
Here's what I suggest.  On the pc with the old drive in it, create a new PST on a flash drive.  Copy the contacts from the original pst to this new pst.  Let it finish and close outlook so the file is closed properly on the flash drive.  
Then put the flash drive in the new pc, open the pst in outlook and copy from the flash drive's pst to your new pst on the new pc.
Hope this helps.  It should work just fine.

First I'd get the contacts out of the old file and into your primary PST.  
What outlook version are you running?  The menus are slightly different for getting the address book as you describe set.

Outlook 2003.    The primary .PST file is the one I brought over from the old hard drive via a flash drive.   How would I get the contacts out of there when it has the Calendar, contacts, and e-mails from the old drive?

Well before I got your last reply, I deleted all the Outlook files off the new drive and tried to import the PST file that I had off the old hard drive.   Now it is asking for a password when I try to open Outlook.  There was never a password involved.   I don't understand why I cannot import the PST file from the old hard drive without all these issues?

Is the password for checking mail?  Try just clicking cancel.  Then follow the instructions 2 posts above and report back.
Be patient, I will continue to help until this works.
 

I got passed the password.   Thanks.   It worked