I was encouraged to turn my comments into an answer by Beqa Arabuli and fossfreedom. I posted the solution first in the comments, but bigbadonk420 just put a similar answer. Nevertheless, because it was my idea initially it is legitimate to put another answer here.

It is most likely not an Ubuntu problem as you have changed browsers, reinstalled the OS and done everything that could reasonably be done. The fact that your ping to profile.ak.fbcdn.net is idle means that your are not resolving the address at all (the ping is not being silently blocked as I can ping it successfully). This means that it is probably a dns related issue; you can resolve facebook.com, but not all its content delivery networks (cdns).

That is why other internet sites are fine, but facebook is affected; there must be some kind of misconfiguration in your isp's dns records, or they are blocking the Facebook cdn for some reason. If they are using a transparent proxy perhaps the facebook cdns are getting swept up with that. Anyway, it is impossible to know the exact reason without contacting your isp.

However, the best thing to do is to try an alternative dns; there are several alternatives, but probably the best is Google dns. More information is available from here; you need to set your primary dns as 8.8.8.8 and your secondary as 8.8.4.4 in your Ubuntu network settings and then reboot. You must make sure that your dns is not automatically being set to your original isp's dns. There are more instructions here relating to the setup of Google dns, but it is straightforward and should allow you to solve your problem without contacting your isp.

Go to network-manager > select your connection > click edit and then select the ipv4 tab (if you are on ipv4 as most people are). The screenshot is below: change automatic dhcp to automatic (DHCP) addresses only and enter the dns details in the box provided: