I have a simple home network of 2 computers running xp next to each
other through a standard switching box. One can see number 2 just fine
and transfer files, but although number 2 can see number one, when I
try to open anything, I get a message that I do not have permission.
This is in spite of having administrator privilages, shutting down the
firewall and sharing everything

How are you transferring the files? Are you using drive sharing?

HI, IN ORDER to access shared folder(s) on another computer (lets say 
PC-A) you should make drive map on PC-B. While making map drive on
PC-B to another computer's share (something like \\pc-a\share) you
should choose option "Connect using a different user name" and then
write this for user name:
"pc-a\usernamefrompc-a" and password from username from PC-A. Remember
this all happens on PC-B. This works also otherway around.
Usually you do not even have to see another computer in "MY neighbours" folder.
Everytime you reboot it will simply reconnect this share through drive
maping and you can transfer the files.