Ok, here's an update to this problem I posted last week....
First of all, thanks to everyone who responded with suggestions and offers.
I didn't get time to call Tom, but was able to find the solution this weekend.
The problem turned out to be with a Cisco VPN Client I had installed on my XP machine a month ago to
allow me to work from home part time. The VPN Client has a Stateful firewall built into it that is always on, even when the VPN Client is not! Thank you very much Cisco!
So this firewall was blocking all ICMP traffic trying to come into the XP machine. This includes echo requests generated by Ping, so no other system on my network could see the XP machine. The problem was actually already there when I tried to connect the new Vista laptop, but because the other machines on my network are used by my wife and daughter and they seldom access the files on the XP machine I was not aware the problem existed.
The solution was to turn off the Stateful firewall in the VPN Client. Fortunately, they put a command in the options control to disable it. Once it was turned off, all was fine and I was able to access the XP files from all points on the local net. I was even able to open a remote desktop on the XP machine fromt he Vista laptop. Worked slick.
This was a nasty one. I spent a hell of a lot of time trying to find this one. On the plus side, I did learn a bit more about networking and cleared up a couple other minor issues that had been in the system.
I'm not a big fan of Vista. They took away some of the features of XP that I have grown accustomed to.
Also, my Vista version is 64 bit, and the Cisco VPN Client only comes in 32 bit so it won't run on the laptop. All that means is I won't have to work this weekend while I'm away for Thanksgiving

Moderators, this message can be moved to OT, if you wish. Thanks for allowing it to stay in the main area for the week.
craig