I have suffered with this issue for 4 days now, where even with a active internet connection the facebook App for Android will report “no internet connection” I finally solved it, first this will require that you have your device rooted, and a copy of Titanium Backup (not sure if you need pro or not, I have pro)
First uninstall Facebook.
Load up “adb shell”
I ran from the /data directory the command rm `find . | grep facebook`
re-install the Facebook App
open up Titanium backup
select Backup/Restore
Find facebook in the list and select it
from the dialog box that comes up select Wipe Data
For me that fixed Facebook for Android. But Facebook needs to fix the root problem what ever it is, as not all users have Root Access (I am lucky I do as I am a geek) A simple uninstall/reinstall should fix it.
I had this exact same problem, but following these steps still didn’t fix it.
Also, I noticed that Friendcaster won’t load the Facebook login either… so potentially I won’t be able to use anything that uses the Facebook login.
Also tried using SetDNS to change to a different DNS server, which also didn’t help (though did seem to temporarily solve other problems I was having, including getting to the Facebook mobile site).
No idea what is going on.