EH, What DSL modem/router is you ISP using and do you have a DSL Gateway/Router connected to it or a HUB?
The reason only one computer can connect is because they are getting their IP address assigned by the DSL modem and it sounds as if it only allows one IP address to be assigned. So both systems end up getting told they are the same system (IP Address) which can not happen. The first to connect to the DSL is the one that works.
You can test this by pulling the rj45 connectors(network cable ends) out of both computers and then plug one in and then the other and see which will connect and which will not.
Do it in reverse and I bet you find that the first one plugged in connects.
If your DSL Modem has multi connectors in the back of it, it should use DHCP to handle multi computers on the local LAN side (your house). But ISP's can be funny that way, they might demand that you pay for extra connections, and the reason there is more than one jack is that they figure you might have more than one computer throughout the house and they allow you one connection from any of the computers plugged into the DSL modem at any given moment.
Most of the time you want to put a DSL/Cable/Network - Firewall/Gateway/Router between your DSL Modem and your computers giving you the ability to connect a number of computers through the one feed (DSL connection). You also want to have hardware protection with at least NAT enabled to stop low level hacking of your systems.
(DSL Modem)--(DSL Router/Gateway)=

Software Firewall/Virus - Computers on your network)
(DSL Modem)
WAN IP Address = assigned by your ISP
(DSL Router/Gateway)
DHCP = Enabled so when your WAN changes this DSL Router/Gateway will update.
WAN IP Address = passed over from DSL Modem which is assigned by your ISP.
LAN IP Address = 192.168.0.1 (depends on what one you have, Linksys defaults to 192.168.0.0, while others default to 192.168.0.1. I'll use the second)
Subnet Mask = 255.255.255.0
(Computer one)
IP Address = 192.168.0.5 (you can change the last number to anything you like starting at 2 and up to 254 as long as it is not the same number as any of the other equipment on your network)
Subnet mask = 255.255.255.0
DNS = Obtain DNS server address automatically (if you know or can find the addresses, you should add them, but it is not a must or shouldn't be)
Metric = Automatic
save and exit...
Do the same on all other computers changing the last number of the LAN IP Address; 192.168.0.8 and so forth. The rest is the same....
You need to make sure that all computers are setup to be a part of the same Workgroup if you wish to share resources and access files and such across them.
Windows defaults to MSHOME so they will be ok unless you change one of them, you need to change all of them to be the same..
Personally I would change them to something only I know because it is a habit to not use defaults for such things. Defaults are well know and people cracking networks always look there first (defaults).
Also passwords are something that you want to consider being creative with. Write them down, do not share them and do not use them anywhere else, including the web.
anyway...
just some possibilities, hope it helps....
oh I added you to my contact list in MSN on this laptop, I keep it close by at all times pretty much and it is always online through wireless, multiplicity_11 is the screen name....
If you want to add me I might be able to walk you through getting the second system online while the first one is online and in an IM depending on the hardware you've got and the setup...
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