Hi all:
    I am trying to connect my Vista Ultimate PC (with beta TV Pack) directly to my X-box360 Core to use it as an extender.  I am using a Belkin CAT6 ethernet patch cable from the Intel gigabyte NIC on the motherboard thru the wall to the X-box360.  My problem is that whenever I turn off, put the pc to sleep or use the "Away Mode" and try to re-connect to the PC,  Vista sees the X-box360 as being in a "Unidentified Public Network" and I have to go into Network & Sharing Center and using the "Customize" feature change it to a "Private Network" before Network Discovery allows the PC to see the X-box360.  The X-box360 then immediately connects and I am able to use all the X-box extender capability. 
    Possible clues to the problem......when I first set up the X-box360 as an extender by clicking "Add and extender" in tasks and then going to the X-box360 and clicking the Media Center button to set up the connection I get a message on the X-box360 saying something to the effect that it was unable to find the "DHC (server?)" and another button saying "continue".  If I follow-up on the failure to find the "DHC (server?)" the network dialogue mentions something to the effect that if I am using an "ad-hoc" connection that the failure to find the DHC(server?) is normal and not a problem.  So,  I go back and click on continue and get the numbers to type into the Vista extender set-up and "Ka-boom", Vista sets up the extender in less than a minute or two and Media Center comes up on the living room tv without any problem......until I close Media Center on the Extender and the PC goes to sleep, shuts down or goes into Away Mode.  (I've tried all three settings). 
    I don't need internet on the X-box360.....I don't play games (too old!) so I only have dial-up internet service to update the guide and check e-mails etc.  I have a feeling that this would be a lot easier if I had broadband and was using a router!  I have tried using a Linsky 5-port switch to link my 4 PCs and the X-box360 extender but the same "Public Network" problem occurs. 
     I didn't have any problems like this using my XP MCE 2005 pc to connect to the X-box360 but I want to use the advanced capability of  Vista (with TV pack) to stream HD to the living room tv.
    Now the question......can someone help this old man figure out the problem?  Or, is it not possible without using a router and/or broadband internet? (Keep in mind,  I'm not too computer knowledgeable!) 

It sounds like the PC and X-Box are both set to use Dynamic IP addresses, but you don't have a DHCP server (normally the job of a router), so you end up using 169.something addresses. It's possible that these addresses change every time, so you keep having to set up again. I'd suggest that you try assigning a static IP address to each of the boxes and see if that helps. Not sure how you do it on the XBox, but on the Vista machine, go to Control Panel Network and Sharing Center Manage Network Connections Right-click on your network card and select Properties, Scroll down to Internet Protocol Version 4(TCP/IPv4) and click on Properties Click on "Use the following IP address" and enter 192.168.10.1, subnet mask 255.255.255.0 leave the gateway blank (or set it to 192.168.10.255 if necessary). On the XBox, set the IP address to 192.168.10.2, subnet mask 255.255.255.0 and see if that makes any difference.

Hello Ripwave:
I tried your suggestion but the Xbox360 also required a gateway address when I tested the connection.  So,  not knowing what to do I tried using the Gateway address you suggested for the PC (192.168.10.255) and then put that same Gateway address on the Vista PC.  Those settings also  reported failed on the Xbox 360.  I set the PC and Xbox360 back to automatic, then after it called it a public network I changed it to Private as before and the two connect fine but Vista still does the same thing after a disconnect.  Thanks for your efforts,  I appreciate it.

What did the XBox say that it didn't like about the settings? Try using the PCs IP address as the Gateway, in case it's looking for a "live" address. (Though it should let you set a static address even if you're not connected to anything). The two machines should have different IP addresses, 192.168.10.1 and 192.168.10.2, the same mask, 255.255.255.0, and don't need a gateway, as they don't need to route any traffic to anywhere else, but if it insists that you enter something for the gateway, any other address in the subnet should be acceptable. Oops, I see that I suggested 192.168.10.255 - that address might not be technically valid. Try 192.168.10.254 instead (or 192.168.10.1).

Hello again Ripwave:
The message on the xbox was the same generic message I got before making the changes as in my first post.  I have gone back and re-set the pc networking to automatic and re-connected to the xbox and will just put up with having to change the network to Private each time I want to turn on the xbox.  Maybe someday I'll switch to broadband and get a router which will probably work better.  If I get too tired of switching the network to private everytime I need to connect to the xbox, I'll just go back to my MCE2005 pc and connect it to the xbox.  It works perfectly but when I upgrade to a wide-screen living room tv I will need Vista to watch HD programming.  Right now I just watch the HD stuff on my pc monitor.
  I don't think Microsoft intended the xbox to be used by someone with dial-up internet and so it just doesn't hook up right.  Too bad, since over 40% of the population still uses dial-up instead of broadband.