Are *any* hosts able to connect via X?
If not, chanced are you need to enable it on the *nix box. Check out the config files in /etc/ X (or X11, or X11R6 ...depends on the flavor of *nix)/ xdm and gdm.
If others can get in, then it's some peripheral parameter, like available fonts, or a firewall.
Most flavors of *nix are delivered with Telnet disabled, and SSH enabled instead. SSH is the same terminal functionality as Telnet, but it's encrypted (SSH also enables some other functions that may be desirable ... like secure FTP and tunnelling).
Find & download an SSH client and try that, or enable telnet on the *nix box (find & run telnetd (that's telnet-DEE).
Since your captured traffic shows no response from the *nix side, I'm going with "You need to enable X on the *nix ox" or you have a firewall in the way.
(Which X server/package are you trying to use?)
Good Luck
Scott