Thanks for being so willing to help out. I appreciate it!!

I was gonna address this last, but I think I had a bit of a
breakthrough at the end of my research so this info is getting bumped
to the top.

The only firewall I have on my machine *aside* from the Cisco VPN
client (more on that in a minute) is Windows Firewall that came with
SP2. Oh yeah, that reminds me: both machines are WinXP Home with the
latest updates installed. Anyway, regarding the Cisco VPN client -
there was a setting in there called "stateful firewall (always on)"
that was CHECKED. I unchecked it and have tried a few things.
NEWSFLASH: I can now ping "brian" from "heidi" by name and by IP. Also,
port requests on my router that are set up to forward to "brian" are
working again as well. Finally, I attempted to map a drive on "heidi"
to a shared dir that resides on "brian" and was able to do so. To me,
that accomplishes everything I have been trying to keep stable. BUT
that raises another question or two: is it safe to disable the
"stateful firewall" on my VPN client? Perhaps I should check with the
IT guys at work?

I'll go ahead and include the remainder of my findings in this post in
case you want to see them and / or there's something else I need to be
aware of. If you consider the problem solved and do not have the time
to review this info, I understand.

Ok, here's what I found with regards to the restrictanonymous presence
in the registry.

on "brian", the following registry dirs had keys named either
"restrictanonymous" or "restrictanonymousSAM." In each case, the value
for "restrictanonymous" was 0 and the value for restictanonymousSAM was
1.

HKEY_LOCAL_MACHINE\SYSTEM\ControlSet001\Control\Lsa
HKEY_LOCAL_MACHINE\SYSTEM\ControlSet003\Control\Lsa
HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Control\Lsa

Furthermore, there were also a pair of dirs that had my search criteria
("restrictanonymous") in the name of the dir itself.

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows
NT\CurrentVersion\SeCEdit\Reg
Values\MACHINE/System/CurrentControlSet/Control/Lsa/RestrictAnonymous

which has the following keys and their corresponding values:

(Default)   REG_SZ       (value not set)
DisplayName  REG_SZ   Network access: Do not allow anonymous
enumeration of SAM accounts and shares
DisplayType  REG_DWORD     0
valueType      REG_DWORD     4

HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows
NT\CurrentVersion\SeCEdit\Reg
Values\MACHINE/System/CurrentControlSet/Control/Lsa/RestrictAnonymousSAM

which has the following keys and their corresponding values:

(Default)   REG_SZ       (value not set)
DisplayName  REG_SZ   Network access: Do not allow anonymous
enumeration of SAM accounts (NOTE: does NOT say "and shares" at the
end)
DisplayType  REG_DWORD     0
valueType      REG_DWORD     4

The registry findings for "heidi" were identical to that of "brian".

Here is the IPCONFIG and BROWSTAT listings for each machine. NOTE: The
"browstat" command does not appear to have worked.

IPCONFIG info for "brian"

Windows IP Configuration

       Host Name . . . . . . . . . . . . : brian

       Primary Dns Suffix  . . . . . . . :

       Node Type . . . . . . . . . . . . : Unknown

       IP Routing Enabled. . . . . . . . : No

       WINS Proxy Enabled. . . . . . . . : No

       DNS Suffix Search List. . . . . . : hsd1.ut.comcast.net.

Ethernet adapter Local Area Connection:

       Connection-specific DNS Suffix  . : hsd1.ut.comcast.net.

       Description . . . . . . . . . . . : VIA Rhine II Fast Ethernet
Adapter

       Physical Address. . . . . . . . . : 00-E0-4C-97-B6-3B

       Dhcp Enabled. . . . . . . . . . . : Yes

       Autoconfiguration Enabled . . . . : Yes

       IP Address. . . . . . . . . . . . : 192.168.15.102

       Subnet Mask . . . . . . . . . . . : 255.255.255.0

       Default Gateway . . . . . . . . . : 192.168.15.1

       DHCP Server . . . . . . . . . . . : 192.168.15.1

       DNS Servers . . . . . . . . . . . : 192.168.15.1

       Lease Obtained. . . . . . . . . . : Thursday, August 25, 2005
10:09:53 PM

       Lease Expires . . . . . . . . . . : Saturday, August 27, 2005
10:09:53 PM

BROWSTAT info for "brian"

'browstat' is not recognized as an internal or external command,
operable program or batch file.

IPCONFIG info for "heidi"

Windows IP Configuration

       Host Name . . . . . . . . . . . . : heidi

       Primary Dns Suffix  . . . . . . . :

       Node Type . . . . . . . . . . . . : Unknown

       IP Routing Enabled. . . . . . . . : No

       WINS Proxy Enabled. . . . . . . . : No

       DNS Suffix Search List. . . . . . : hsd1.ut.comcast.net.

Ethernet adapter Local Area Connection:

       Connection-specific DNS Suffix  . : hsd1.ut.comcast.net.

       Description . . . . . . . . . . . : Compaq NC3161 Fast Ethernet
NIC

       Physical Address. . . . . . . . . : 00-50-8B-D7-6B-F6

       Dhcp Enabled. . . . . . . . . . . : Yes

       Autoconfiguration Enabled . . . . : Yes

       IP Address. . . . . . . . . . . . : 192.168.15.101

       Subnet Mask . . . . . . . . . . . : 255.255.255.0

       Default Gateway . . . . . . . . . : 192.168.15.1

       DHCP Server . . . . . . . . . . . : 192.168.15.1

       DNS Servers . . . . . . . . . . . : 216.148.227.68

                                           204.127.202.4

       Lease Obtained. . . . . . . . . . : Thursday, August 25, 2005
10:07:07 PM

       Lease Expires . . . . . . . . . . : Friday, August 26, 2005
10:07:07 PM

BROWSTAT info for "heidi"

'browstat' is not recognized as an internal or external command,
operable program or batch file.

 So there you have it. All I have done here is compile information; I
did not edit any registry entries because from following the guide you
provided on the restrictanonymous aspect of the registry, it did not
look like editing anything was neccesary. I included the search
findings here in case you needed to peruse them.