I'm having a problem getting my head around this one.
You start off by saying, you have a wireless network, but then talk about telephone cables to each machine and continue by referring to a modem/router.
Let's try and dissect this a little.
First, as regards NetMeeting, all I can offer is to disconnect the firewalls for a few minutes and see if it then works. You MUST rule out firewall problems before getting involved with others. I have found networking in XP can be a pain to set-up. One time it will work with no problems, other times, it takes forever to sort out. XP home seems to be more difficult when things go wrong than XP Pro, as you don't have the flexibility the Pro version offers.
Networks and Internet connection.
If you are connecting via a modem/router, it is only this device that needs to be on for each individual computer on the network to access either the network or the Internet. It is only if you are using a form of Internet Connection Sharing (ICS), the gateway machine needs to be connected.
The length of cable should not make a great deal of difference to a Broadband connection. It would only (possibly) be relevant, if your connection was already on the physical distance limit entering your home. But if you are using a Wireless modem/router, why not just place it next to a convenient telephone socket?