Exim Mail Transfer Agent can't deliver mail - email

Question

I have problem with exim MTA, it can not send any mail.
I have followed a simple and straight forward guide in how to setup the MTA : https://library.linode.com/email/exim/send-only-mta-ubuntu-12.04-precise-pangolin
But when I test the configuration at the end it fails to send.
I don't get any error message when issuing the commands :
echo "This is test 1." | mail -s Testing_1 myemail#gmail.com
echo "This is test 2." | mail -s Testing_2 myemail#hotmail.com
But I can read in the log (/var/log/exim4/mainlog) that it was not successfully sent (and I don't receive any of the emails).
What should I do, I have no idea about what's wrong...??
My first thought was that the router (or firewall) was blocking my MTA, but the log shows that it has been in contact with the out side, so I don't think tht is the issue
I appriciate all the help I can get.
Edit : I had to use ISPs mailhost by setting config : dc_smarthost='mailout.isp.com' and adding a rewrite rule for Exim, matching my email adress for the account with the ISP.
/John
exim4.conf-file (/etc/exim4/update-exim4.conf.conf):
dc_eximconfig_configtype='internet'
dc_other_hostnames='PandaBoard; mydomain.net; meetup; localhost.localdomain; localhost'
dc_local_interfaces='127.0.0.1'
dc_readhost=''
dc_relay_domains=''
dc_minimaldns='false'
dc_relay_nets=''
dc_smarthost=''
CFILEMODE='644'
dc_use_split_config='false'
dc_hide_mailname=''
dc_mailname_in_oh='true'
dc_localdelivery='mail_spool'
Exim4 Log:
2013-09-13 00:13:35 exim 4.76 daemon started: pid=17823, -q30m, listening for SMTP on [127.0.0.1]:25 [::1]:25
2013-09-13 00:13:35 Start queue run: pid=17825
2013-09-13 00:13:35 End queue run: pid=17825
2013-09-13 00:23:11 exim 4.76 daemon started: pid=18570, -q30m, listening for SMTP on [127.0.0.1]:25 [::1]:25
2013-09-13 00:23:11 Start queue run: pid=18572
2013-09-13 00:23:11 End queue run: pid=18572
2013-09-13 00:24:17 1VKFJB-0004pm-Uf <= john#mydomain.net U=john P=local S=404
2013-09-13 00:24:18 1VKFJB-0004pm-Uf gmail-smtp-in.l.google.com [2a00:1450:4008:c01::1b] Network is unreachable
2013-09-13 00:25:22 1VKFJB-0004pm-Uf gmail-smtp-in.l.google.com [173.194.71.26] Connection timed out
2013-09-13 00:25:22 1VKFJB-0004pm-Uf alt1.gmail-smtp-in.l.google.com [2607:f8b0:4003:c02::1a] Network is unreachable
2013-09-13 00:26:26 1VKFJB-0004pm-Uf alt1.gmail-smtp-in.l.google.com [173.194.64.27] Connection timed out
2013-09-13 00:26:26 1VKFJB-0004pm-Uf == myemail#gmail.com R=dnslookup T=remote_smtp defer (101): Network is unreachable
2013-09-13 00:46:26 exim 4.76 daemon started: pid=19280, -q30m, listening for SMTP on [127.0.0.1]:25
2013-09-13 00:46:26 Start queue run: pid=19282
2013-09-13 01:03:55 1VKFvX-00052n-9V <= john#mydomain.net U=john P=local S=402
2013-09-13 01:05:00 1VKFvX-00052n-9V mx3.hotmail.com [65.54.188.94] Connection timed out
2013-09-13 01:06:04 1VKFvX-00052n-9V mx3.hotmail.com [65.54.188.72] Connection timed out
2013-09-13 01:07:08 1VKFvX-00052n-9V mx3.hotmail.com [65.55.37.72] Connection timed out
2013-09-13 01:08:13 1VKFvX-00052n-9V mx3.hotmail.com [65.55.92.136] Connection timed out
2013-09-13 01:09:18 1VKFvX-00052n-9V mx3.hotmail.com [65.55.92.168] Connection timed out
2013-09-13 01:09:18 1VKFvX-00052n-9V == myemail#hotmail.com R=dnslookup T=remote_smtp defer (110): Connection timed out
2013-09-13 01:16:26 Start queue run: pid=19436

Answer 1

Looks to me like your ISP has blocked connections outbound to tcp/25. Why did you reject your initial supposition that it was the firewall? The logs you quoted indicate that your server can make DNS requests, but there are no successful attempts to connect to a mail server. It could still be a local firewall issue but these days its very common for ISPs to prevent their clients from sending email to tcp/25 unless you have explicitly requested the ability to do so (and sometimes not even then).
Take exim out of the equation and run this from the command line of your mail server:
telnet 65.54.188.94 25
if you can connect, it's a problem with your exim install. If you can't connect, it's a network issue, whether a local firewall, ISP firewall, etc.

Answer 2

Use should check to see that any firewall(iptables, csf...) is running on your server first.
If yes, turn it off and try to test telnet to external mail server like :
telnet external_mail_server 25
If ok, you should check the exim configuration.
If no , you should contact your hosting provider