It's been a few years since I personally used ICS and I don't have a WinME system any more, so I can't make screen shots of what you should see and do. But here is what I remember generally...
You indicate your router is giving out addresses starting at 192.168.2.101. That suggests to me that it has assigned itself an address of 192.168.2.1. You indicate the wired desktop got 192.168.2.102. That suggests something else got 192.168.2.101 - probably the wireless connection winging in from upstairs. Check it to be sure, but in some ways it doesn't matter that much. The router's DHCP server will issue addresses in the order that they are requested by systems as they boot. Therefore, it could happen tomorrow that the wired desktop is the first on and it will get 192.168.2.101 and then the wireless ME system, when it is started, will acquire 192.16.2.102. The router keeps track of who has what when, so don't worry.
Now we have to configure the ICS upstairs. Here is a link to a webpage about networking and setting up ICS on a WinME system:
http://www.practicallynetworked.com/sharing/ics/icsmeinstall.htm
As you read through the tutorial, make the following mental changes for your situation. When the tutorial speaks of ''connecting to the cable modem,'' think to yourself ''connecting to your router'' (which in turn connects to your cable modem). On the page of the Windows Networking Wizard that asks if this computer connects to the internet, choose the button for ''A direct connection to my ISP using the following device'' and then pick your wireless adapter from the list. On the next page of the Networking Wizard for setting up connection sharing, click the yes button and specify the wired ethernet adapter as the device which connects to your home network. Note that this is where you will probably be thrown off by the terminology. You are probably thinking of all your downstairs stuff as your home network. Well, it is, but not from the viewpoint of the WindowsME system's instance of ICS. From its perspective, downstairs is the wide area internet while the local ''home network'' is the all the wired upstairs stuff that it will be in charge of (actually, only the PS2, but don't deflate the WinME's ego by mentioning that it doesn't have your whole world under its command...
) Click on through to Finish the wizard. You don't have to make a client disk - there wouldn't be anything to do with it. You'll probably have to reboot the WinMe system.
Now here is what your numbering systems will look like: The router will acquire your ISP's public IP, set itself as a gateway using 192.168.2.1 for itself, and then issue 192.168.2.101 (or .102) to the WinME system's wireless adapter. WinME ICS will then treat that IP as if it were the public IP (though it really isn't a routable public IP), set itself as the gateway for all upstairs systems using 192.168.0.1 for itself, and start issuing addresses out through its ethernet port starting at 192.168.0.2. Finally, the PS2, which should now have IP address 192.168.0.2 will connect back to the WinME ICS which will translate that to what it thinks is the internet coming in through the wireless adapter on IP address 192.168.2.101, which will zing down to the router, which will translate it again to the real public IP address it got from your cable modem.
The key here is that Windows ICS defaults to using addresses in the 192.168.0.xxx range. I may remember incorrectly, but I don't think you can tweak the address range it uses, you're stuck with 192.168.0.xxx. That means you have to make sure that your downstream router is set to use a different range, such as the 192.168.2.xxx range you're already using on the router. Otherwise, the DHCP server in the router will argue incessantly with the DHCP server in WinMe ICS about who's in charge of what and who already has addresses that the other thinks belong to it.
So there you go, have at it...
dw