"With the new Vista interface, when I look into the network connections I see that it only gives a "Local Only" access. The other system gives a "Internet and Local"."
That is simply reflecting the absence of a default gateway. This does not provide any additional information than seeing you're an IP address via APIPA. IE, it is not a part of the problem. It is simply telling you in a more intelligible fashion you have no internet connection.
When you switched out the connection to the cable/dsl modem or whatever, did you turn off that device off for one minute, and then turn it on? You may also then need to turn off the newly connected computer, wait a minute, and turn it back on.
"Enough, enough bowing down to disillusion!
Hats off & applause to rogues & evolution!
The ripple effect is too good not to mention.
If you’re not affected, you’re not paying attention!"