I assume that you've actually shared some disks or folders on each
computer.
Try accessing the other computer by typing its name in the Start | Run
box in this format:
\\computer
If that succeeds (shows shared disks and folders), you can create
shortcuts to them by going to My Network Places and clicking "Add a
network place". If that fails, keep reading.
Since the computers can ping each other, I don't think that ZoneAlarm
is causing the problem. However, it wouldn't hurt to un-install
ZoneAlarm while troubleshooting. I assume that your residential
gateway is a typical home broadband router. Those routers act as
firewalls, preventing Internet hackers from accessing your computers.
You didn't say whether the computers can ping each other by IP
address, computer name, or both.
If they can ping each other by IP address but not by computer name,
there's a problem with NetBIOS name resolution. In that case, these
steps should help:
1. Use only one protocol for File and Printer Sharing. If the network
needs more than one protocol, unbind File and Printer Sharing from all
but one of them. Details here:
Windows XP Network Protocols
http://www.practicallynetworked.com/sharing/xp/network_protocols.htm
2. Make sure that NetBIOS over TCP/IP is enabled on each computer:
a. Open the Network Connections folder.
b. Right click the local area network connection.
c. Click Properties.
d. Double click Internet Protocol (TCP/IP).
e. Click Advanced.
f. Click WINS.
g. Click the Enable NetBIOS Over TCP/IP button.
3. Run "ipconfig /all" on each computer and look at the "Node Type" at
the beginning of the output. If it says "Peer-to-Peer" (which should
actually be "Point-to-Point") that's the problem. It means that the
computer only uses a WINS server, which isn't available on a
peer-to-peer network, for NetBIOS name resolution.
If that's the case, run the registry editor, open this key:
HLM\System\CurrentControlSet\Services\Netbt\Parameters
and delete these values if they're present:
NodeType
DhcpNodeType
Reboot, then try network access again.
If that doesn't fix it, open that registry key again, create a DWORD
value called "NodeType", and set it to 1 for "Broadcast" or 4 for
"Mixed".
For details, see these Microsoft Knowledge Base articles:
Default Node Type for Microsoft Clients
http://support.microsoft.com/default.aspx?scid=kb;en-us;160177
TCP/IP and NBT Configuration Parameters for Windows XP
http://support.microsoft.com/default.aspx?scid=kb;en-us;314053