Wired home net, 5x router - 4 to computers, 1 to new cable modem: connect?

Question

I have an in-home Ethernet, cat-5 wired, network to which are connected 2 Macs and 1-2 Windoz boxes. I just subscribed to cable high speed internet service (Comcast nee Adelphia) and want direct access from each computer to the cable modem. Supplier sez this should work - however, their tech support doesn't have wired net solutions in their 3 ring binders (you'll have to consult the router mfgr - well, the router, GFE EZ500-S, is no longer made but all seems to be working fine - I can ping the working machines from this Mac, all given a common subnet IP address of 10.10.10.nn, nn=1/2/3/4. My g4 mdd nn=2.
The cable modem is broadcasting just fine - a Motorola 5100 model. All lights are green that should be. I understand that if I directly hooked it to one (probably Windoz) box I would should see the default webbrowser displaying the Adelphia signin screen by which I initiate my account name and email identity. I know from the Compaq box with XP home on it and the Help file that Billy Gates recommends AGAINST what I want to do and wants me to put a router on my router through which every other (than the 1st) box must go to get to the cable. The cable modem is connected directly to the 5th RJ45 port on the wired router.
My question is, what must I do on the Mac to process the cable modem signals on the Mac? I have it on the authority of an Adelphia geek I chatted with at their local office where I went for face time with them that I need to be walked through Mac connection but that what I want in respect to direct access from each computer to the cable modem should work just fine AS SOON AS I PROPERLY INITIATE SERVICE by interacting with their signup web page on some box. I have not properly configured the Compaq because I am not getting the defaut web browser (Firefox) displaying the Adelphia sign-in. I apparently need to add/activate some XP code to detect the cable modem signal on the Ethernet connection. I haven't done that yet because I'm afraid Billy Gates will compel me to install their router-on-a-router solution.
I am in an unresolved circle here. When I spent 45 minutes on their support line I essentially was told they don't do wired routers/home networks. Tell me, doctor, what should I do?

Answer 1

Duane is correct, the EZ500-S is an Ethernet switch, not a router.
If you want to use your switch to connect your systems to your ISP, then all of your systems must be configured to obtain their IP-addresses automatically*, and you must arrange with your ISP to lease enough IP addresses for all of them. When each system boots, it will use DHCP to request an IP-address from your ISP.
If you don't want to pay your ISP for more than one IP-address, then you must get a router. This isn't Billy Gates' rule, it's the Internet's. If you do this, you can continue to statically assign IP-addresses (10.10.10.nn) to your systems if you want; the router will get its own WAN IP-address from your ISP using DHCP, and you can configure your router to do whatever you need on your LAN. Most routers come with built-in DHCP servers for the LAN, so you could also configure your systems to obtain their IP-addresses automatically -- it's up to you. The router will use NAT to substitute its own WAN IP-address on packets going out to the WAN, and to route incoming packets to the proper system on your LAN.
*unless you contract with your ISP for one or more static IP-address, which is typically a lot more expensive!