Do two computers, connected to the internet by one wireless router,
show only one I.P. address ?

Yes.  There is simply no other answer. Let me try to explain in a metaphor.

Your router IS the IP address.  Your router "brings the internet" to
you like the postman brings mail.

Let me give you an example. Say you live in a city called Internet. In
"Internet City" you want to go to a friends house, so you head to the
address:   123 Any Street (THIS IS THE IP ADDRESS SEEN BY OUTSIDERS,
LIKE A MAILING ADDRESS),   when you get to "123 Any Street" you
remember that your friend's building at 123 Any Street has several
units inside the security of the locked exterior door (THE ROUTER),
although your friend lives at the address, a doorman (DHCP) tells you
to go to Apartment 17 (THE INTERNAL IP ADDRESS - NAT),

All apartments inside this building have the same mailing address (THE
SAME IP ADDRESS), the difference is, when the postman brings the mail
(WHEN THE ROUTER BRINGS VISITORS, YOU CLICKED A LINK AND REQUESTED A
WEB PAGE BE SHOWN TO YOU), the results are shuffled to whatever the
internal address the request came from (Computer 1, Computer
2,...etc.) that the mail was originally sent from (APT 17, 18, 19) 
etc.

Does that make any sense?

A ROUTER (wireless or not) is like the mailman. He delivers what was
sent to you, TO YOU, instead of your neighbor (ANOTHER COMPUTER IN THE
SAME IP ADDRESS AS YOU).


If you don't understand this, and would like me to add supporting
links that could explain it differently, let me know and I'll be happy
to find them...

~~Cynthia

Just a clarification: Each computer on your home network still has its
own IP address from the "private" range (most likely 192.168.x.x),
otherwise they would not be able to talk to the router or to each
other. If you open Command Prompt and type "ipconfig" (for Windows
2000/XP) or "winipcfg" (for Windows 9x), it will show the IP address
of the computer.  These IP addresses will be different on different
computers.
 
If you go to a Web-site that displays the "public" IP address of your
Internet connection (for example, www.myipaddress.com), then you will
see the same address regardless of what computer on your home network
you're using.  It will be the  public IP address of your router, as
was explained in the answer.

When your computer is connected to the internet without a router, your
Internet Service Provider gives out an IP address that goes to your
computer.  This is the IP that your computer functions with, and
allows you to do various things from playing online games to file
sharing.

Now, your ISP doesn't care how many computers you have.  It's just
going to give you one IP address.  IP addresses have to be unique on
the internet.  And, here's where the router comes in.

So you have your DSL or cable modem connected to a router, which then
connects to your two computers.  Your ISP sends you your IP address,
but instead of going to your computers, it gets 'caught' by the
router, so it's now your router's IP address.  The router then assigns
private IP addresses to each of your computers (such as 192.168.0.100,
and 192.168.0.101).  These two IP addresses can only be accessed by
your home network.  They don't even exist out in the internet.  Your
computers now function on the internet through your Router.

So, when you make a request to the internet (such as accessing a web
page or something), the computer sends the request to the router.  The
router does the job, asks for the web page, and the web page is sent
to your router's IP address (this is your public IP).  Then the router
sends the info back to the computer that requested it.

To answer your question more directly:  To the internet, your two
computers don't have an IP address;  your Router has one.  To your
router, however, both of your computers have an IP address.  Showing
your computer's IP address is worthless, because that's a private,
local area address that can only be accessed through your LAN, not the
internet.

Now, routers actually have TWO IP addresses.  They have their public
(WAN - Wide Area Network, ie the internet) IP address, which is given
to you by your ISP, and they have their private (LAN - Local Area
Network, your home network) IP address.  A router's settings can be
accessed by typing in its private (LAN) address in your web browser. 
If it's a Linksys, it'll probably be "192.168.1.1".  This IP can only
be accessed though your LAN, and not by anyone on the internet
(barring hackers and whatnot).

By logging into your router, you can see the router's local IP
address, and the public IP address given to you by your ISP, as well
as seeing what IP addresses it has given out in your LAN, which will
be 192.168.1.100, 192.168.1.101, and so on.

If you have some specific issues (such as if you're having trouble
playing internet games) I'd be happy to answer those too.

Having trouble setting up internet game server (MOHAA)on D-link
router.  I've put all the ports into the router that need to be
forwarded and open as well as XP's firewall.  But still can't find my
server on GameSpy.  I can find it on AllSeeingEye but its using my
private ip not the public ip.