A complicated one:

On the ground floor of my home, I have a Verizon DSL modem to which I
connected a router to share the DSL feed.
On the ground floor through that router one computer is connected to the
internet and runs XP Pro.

On the first floor, I have 3 PCs (all running XP Pro), one laptop (running
Me) and one Mac feeding off the router on the ground floor to connect to the
internet.

I am right now on my laptop and in this room have one of the 3 PCs running
XP Pro. These two machines I have created a network place called MINE. In my
Network Places from the Me laptop, I double-click Entire Network and can see
three different Network Places:

MSHOME (the PC on the ground floor), MINE and WORKGROUP (two other PCs on
the first floor).

From the laptop, if I double click MINE I can see my laptop and the desktop
in this room sharing this network place.
From the laptop, if I double click MSHOME, I can see the PC on the ground
floor and I am prompted for a password to access it.
From the laptop, if I double click WORKGROUP, I can see the 2 other PCs on
the first floor and am prompted for a password to access either one.

My question:
How can insure that my laptop and my PC in this room cannot be accessed from
the other machines at all (reason why I created a different Network Place
but I suspect MINE is visible to the other machines if browsed through
Entire Network) or only through a password?

Thank you in advance for the help.