How to connect to another computer through the Internet using ssh?

I have Ubuntu 13.10 on my laptop which I would like to use to connect to my Ubuntu 12.04 desktop. I installed the open ssh server on the desktop machine using:

sudo apt-get install openssh-server

I checked that the server is running:

sudo service ssh start

and I get:

start: Job is already running: ssh

Next I checked if there is a firewall using:

sudo ufw status

and I get:

Status: inactive

Next I found out the desktop's IP address by executing:

ip addr | grep inet

and I get:

inet 127.0.0.1/8 scope host lo
inet6 ::1/128 scope host 
inet 193.51.236.62/24 brd 193.51.236.255 scope global eth0
inet6 fe80::21a:a0ff:fe10:e8da/64 scope link 

So I suppose that 193.51.236.62 is my IP address.

Then on my laptop I verify that 193.51.236.62 is pingable and then I do:

ssh -v [email protected]

and I get:

OpenSSH_6.2p2 Ubuntu-6ubuntu0.1, OpenSSL 1.0.1e 11 Feb 2013
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 19: Applying options for *
debug1: Connecting to 193.51.236.62 [193.51.236.62] port 22.

And nothing else seems to be happening. Please, how can I troubleshoot this problem? What am I doing wrong?

EDIT:

I can safely ping the server machine:

martin@martin-Studio-1537:~$ ping -c3 193.51.236.62
PING 193.51.236.62 (193.51.236.62) 56(84) bytes of data.
64 bytes from 193.51.236.62: icmp_seq=1 ttl=61 time=2.82 ms
64 bytes from 193.51.236.62: icmp_seq=2 ttl=61 time=4.05 ms
64 bytes from 193.51.236.62: icmp_seq=3 ttl=61 time=4.08 ms

--- 193.51.236.62 ping statistics ---
3 packets transmitted, 3 received, 0% packet loss, time 2002ms
rtt min/avg/max/mdev = 2.823/3.653/4.082/0.587 ms

EDIT2:

I tried to diagnose the connection using nmap as suggested:

martin@martin-Studio-1537:~$ nmap 193.51.236.62

Starting Nmap 6.40 ( http://nmap.org ) at 2014-01-31 18:39 CET
Note: Host seems down. If it is really up, but blocking our ping probes, try -Pn
Nmap done: 1 IP address (0 hosts up) scanned in 3.06 seconds

and then:

martin@martin-Studio-1537:~$ nmap -Pn 193.51.236.62

Starting Nmap 6.40 ( http://nmap.org ) at 2014-01-31 18:40 CET
Nmap scan report for 193-51-236-62.lille.inria.fr (193.51.236.62)
Host is up (0.0056s latency).
Not shown: 998 filtered ports
PORT     STATE SERVICE
3128/tcp open  squid-http
8080/tcp open  http-proxy

Nmap done: 1 IP address (1 host up) scanned in 8.18 seconds

Solution 1:

Start by checking to see that you can ssh into the desktop from the desktop.

ssh 127.0.0.1

If that works, I would check to see if the outside IP and internal IP are different.