Check your router's hardware firewall for block-site rules; you can access it by visiting the router's ip from your browser in the form 192.168.x.x, try:

• 192.168.0.1


• 192.168.1.1


• 192.168.1.25x etc.

Write ifconfig (ENTER) in a console (xterm is fine) and watch the form of the inet address camp, you will need to edit only the last digits to find your router's ip.

You will need to know the password and the user (ex. admin admin, password password, admin password ecc. if you left the default). If you don't know there is a list online, google it...

You must own the router. ;-)

If there is no firewall block - strange - run form a console sudo nano /etc/hosts and remove any line with wordpress inside. Do not edit other lines, it can cause software problems.

A diagnostic action is running tracepath wordpress.com to discover where is the block, if it is a total block and not an http-only block.

Let us know by commenting under here, you can be useful to the community.
Nice evening, I will help you if you need more help.

EDIT for Adame: I must use a solution valid for all users, so you will need patience, network problems are hard to solve.

Execute in a terminal:

echo "127.0.2.X HOSTNAME" >> toadd.txt

echo "127.0.0.1 localhost" >> toadd.txt

(replace hostname with the output of the hostname command and X with the end of your current IP, you can see it in ifconfig)

then edit /etc/hosts as root (use sudo YOUREDITORNAME /etc/hosts and add on top the content of toadd.txt).

Delete toadd.txt :)

Now the first problem should be fixed.

Check if your hosts file is like this:

127.0.0.1 localhost

Y.O.U.R.I.P YOURHOSTNAME

and a comment line.


Other argument.

The ping isn't a valid check because a modern and well configured server will discard your pings to avoid ping bounce network attacks. For example my ping fails on wordpress.
ICMP Ping is good only for well known servers!

But, tracepath shows that no intermediate server receives your ping, and this is strange, because after your router the ping gets lost but continues to "hop"... are you using the network of your factory? If it's it, you can be behind a blocking intermediate server and you will need to use a proxy.

If this isn't you case, let's continue by ignoring tracepath (the path changes always, but your network path appears to be faulty).

Do a next step and try to do from a terminal wget wordpress.com and after that ls -lh: if you see an index file in html format which is greater than 10kb (may change in future) the problem is in your web browser (bad extensions or misconfiguration), if you don't, try other two times.

If you get a good index file (try to open it with a browser by double-clicking it) and you can see the webpage, simply disable ALL extensions in your browser and after that reinstall it.

If you can't get a good index file the problem is in your network.

Here the hard procedure if you didn't solve:

• Disable any proxy set in your browser and remove any instance of Tor
  and Privoxy, or of other distributed anonymous network systems.
  Reinstall them later if they aren't the problem, they are good for
  your privacy.
  


• If it doesn't work change the DNS in your router (not in your PC) to Google DNS (in Google we trust & we find the DNS ip) and try. SUGGESTION: leave the Google DNS, they are always good.


• If it doesn't work let's do a last check you can try to use a transparent proxy (anonim are slow) to re-route your traffic to wordpress: if it goes a server in the newtork hop path is faulty or your ip range is banned. If it doesn't function you may have a block inside your network.
  
  
  It's the best I can do with the information you left, good luck. Let me know. :)
  
  PS: a suggestion, for a proxy list search on google and pick a proxy with LOW ping and HIGH uptime.