Looks like they are trying to use the same ports on both machines. In
Setup/Connection you can change one from 6346 to anything else. Then you
can adjust your firewall and router port forwarding to match the new port
number. The same goes for any of your other P2P software. Make sure each
has it's own unique port.

In freepeers.ini, try reversing the following option:
(Stop BearShare before you open the file or your changes will be lost.)
[Hosts]
bNativeCompletionPorts = Yes ; Use native completion ports for socket I/O

If these don't help, uninstall ZoneAlarm, reboot and test BearShare and your
other P2P software again. That company never really fixed that problem with
packet fragments arriving out of order and it got worse when XP came along.
BearShare and other P2P software have also been using UDP more and more
over the past couple of years which made ZoneAlarm's notorious weakness
stand out.

By the way. There have been so many advances between BearShare 4.5 and
5.1 that you really can't afford not to try the beta I posted. Some of those
advances are in low-level networking code specifically to accommodate XP,
especially SP2, which made a change in it's TCP networking driver to limit the
rate at which a program can open new connections. Since your copy of
BearShare is so old it appears likely that your other P2P apps also predate this
important change in the OS. Kazaa definitely never survived long enough to
make the change. Update all of your P2P apps if you can and if there is still
one you cannot go to www.lvllord.de and download his Event 4228 patcher,
which will let you adjust the connection rate upward.

Just before I start, one more question....

I never use any P2P program simultaneously on both computers. Given this, I assumed that using the same ports wouldn't be a problem. Right?

As part of my previous problem solving, I adjusted the listening port on my torrent program. It didn't make any difference. I still couldn't connect regardless of which port I used. That's part of the reason that I thought the problem was WinXP rather than the P2P program, router or port.