I have been given access to a Airport network (my MAC is in the list
of accepted Macs and I have the proper WEP).
However, I am unable to see the printer that is plugged into the USB
port of the Airport router when I got into network neighbourhood.  I
am not able to see the router through network neighbourhood although I
can see it through Airport Administration client (version 4.2 build
V420.31) running on my thinkpad.
The power book that is also connected wirelessly to this router is
able to print to the printer in question so it is definitely working.
I have Airport Administrator installed on my thinkpad and am able to
log on to the router.  I have gone into Airport - Base station option
and can see the printer from this interface but there is no web
address given for the printer just the "name" and "kind" which is
"Epson Stylus CX6600" for both.

How can I print from my thinkpad without physically connecting the
printer to my laptop.  i.e. how can I use my wireless connection to
the Airport router to print on the printer that is plugged into the
USB port of the router, like the Powerbook G4 does.

Hello Optik_nerd,

I am going to assume you have a recent version of Microsoft Windows
(e.g., 2000, SP) - if not, please make a clarification request and I
should be able to get you a solution for an older version of Windows
as well.

With the newer versions of Windows, the easiest solution for your
problem is to download "Bonjour" for Windows as described at
  http://www.apple.com/macosx/features/bonjour/
This page describes Bonjour in general and has a link for the download
in the lower right of the page (you may have to scroll down to see
it). The download is also available at
  http://www.apple.com/support/downloads/bonjourforwindows103.html

There is a more complete description of this at
  http://images.apple.com/macosx/pdf/MacOSX_Bonjour_TB.pdf
(scroll down to page 6 of this second reference).

Note also that your Windows machine may have to be adjusted if you are
using a third party firewall product (not the Windows firewall). Make
a clarification request if you need specific instructions for your
firewall product.

To find additional information related to this and similar solutions,
search with phrases like
  windows 2000 apple airport printer
  bonjour windows 2000
(or replace 2000 with SP or whatever version of Windows you are using)

Good luck with your network and system set up.

  --Maniac

Answer was bang on, articulate and made it clear that if it did not
resolve the issue that additional info would be made available.