Typically, your DSL "modem" would be plugged into the "WAN" port on a DSL "router". These DSL routers are really multi-function boxes: switch/hub, firewall, DHCP server, maybe print server, and so on. Most of these have 4 to 8 ports for connecting LAN equipment (i.e., PCs, MACs, Linux, etc.). They are all easily expandable just by cascading plain hubs off of them. They use NAT and PAT for address translation and typically work flawlessly with DSL and Cable Internet connections. The client software is removed from all of the systems on the LAN (the "EZ Connect" or whatever stuff), and the router is configured with the required protocol (typ. PPPoE for DSL), user ID and password for quick and easy connection.
In this setup, you would not need to be running any specific software on any one of your PCs. All you need is to have your DSL "modem" and router up for any of your systems to access the 'Net (and to print if your router is also a print server.
I like this setup a lot, sinceit means that I don't have to leave MY system running just so the kids can slough around with Napster, which enhances my impression of security. "Shields Up!" (www.grc.com) tested my connection and we came out invisible, despite my running HTTP and TFTP servers on my home LAN!
If your LinkSYS box is truly just a plain hub, then I recommend you look into getting their DSL router. There are other brands (Asante, D-Link, etc.), but for your situation, you'll probably want to add the EtherFast 1-Port Cable/DSL Router (BEFSR11), and hang your hub off of that. Disable ICS, and the DSL connection software on your WinME box, and configure the router according to the LinkSys documentation.
And there you have a real nice setup.
BTW: DSL is not ATM in most areas. To confuse things, it's much more like ISDN (being digital over copper - at least for the last few metres/feet).