There is probably an interaction between XP and ZoneAlarm that doesn't exist in
Win98 since the TCP stack is three generations apart.
Have you tried uninstalling it yet?

OK. I'm bewildered!

I previously said that I prefer to understand what and why I'm doing something. I don't understand but it is working now.

Here is a seriously abbreviated version of what I had previously done:
-installed various P2P & torrent programs - they wouldn't connect on the XP machine
-uninstalled both ZoneAlarm & AVG virus scanner - they still didn't work.
-reinstalled both ZoneAlarm & AVG virus scanner - they still didn't work

Here is what I just did:
-disabled ZoneAlarm (not uninstalled), tried BearShare - didn't work
-uninstalled BearShare 4.5.0.63, installed BearShare 5.2.5 - It WORKED!
-re-enabled ZoneAlarm - It still works!
-I checked the bittorrent client in Opera and it now works too!

It doesn't make any sense and I don't understand why but it is working.

BTW - Once it was working, I checked my event log and found one 4226 entry - (TCP/IP reached connection limit). I presume that I should use lvllord to increase the number of half open connections. What number would you recommend?