Unwanted ICS services showing up, system disappears

My home network consists of 2 XP Pro SP3 desktops (D06 and D07)and a XP Home
SP3 with a dlink router, a verizon dsl line, all hardwired with CAT5 wiring.
After several years of having a successful network, sharing a printer and
files, about 2 weeks ago the shared printer went off line to one of the
desktops and the laptop. Since I already had a printer cable in place to
provide for printing in case the desktop it is usually attached to was not
on, I just swapped the cable and went on. Then, a few days later I went to
do backups (machine to machine) and discovered that the machine, D06, with
the printer was not accessible to the other two machines. However, it could
see the other two systems (shared files and a network disk). In looking at
Network Connections, I discovered that along with the LAN connection, an
Internet Gateway connection that is used for a shared internet connection,
was coming up as well. The box on the properties tab which tells it to
display itself in the tray was blank and after checking it, I can now see
both the LAN connection icon and the Internet Connection icon. This device
has some interaction with Windows Firewall. If I turn on WFW and enable the
LAN connection, just the LAN connection comes up. If I then go to Change
Windows Firewall Settings and turn the firewall off, then the Internet
Gateway comes up. I don't know what this means, but thought it might hint to
something.

Also, when I run Windows Explorer on D06, the problem machine, the files on
it that are marked as shared and modifiable do not show under the My Network
Places -- this is different from the other two machines. Also, I can ping
all three systems as well as the router: 192.168.0...100, 101, 102, and 1. I
have forced the router to reboot, but no change. I have run the Network
Wizard about 50 times without any luck. I do not remember having set up ICS
or ICW, so I don't know where they are coming from. I run Zone Alarm on D06,
the machine that is malfunctioning. I am not the only user of the system,
but our use is conservative and have not had any problems with malware so far
(maybe now?) . There has been no noticable effect on my ability to reach
the Internet through any of the three machines.

Any suggestions? I would like to know how to remove the ICS false
connections and re-establish my network. And of course, I wonder how this
might have happened.

I looked through the questions for a similar problem but did not find
anything quite the same.

Thanks in advance for your help.