Kyle,
I think this case may be closed.
The two servers were running on the same PC which was in a LAN. Probably in that LAN there is a Sisco router that does some ports filtering.
Also pinging that server PC from ouside LAN did not work.
Solution:When I moved my datasocket server to a different environment (beyond my current LAN) the server communicated well (over internet) with my client datasocket PC (pinging also worked there).
Andrzej