I am having the same problem. Every time I try to login to my Facebook app for Blackberry 9650, I get an error that reads, ""A connection cannot be established to the Facebook server." If I type the wrong password, the app recognizes it and tells me so. It is confusing to me that the app can connect to the server to know whether my password is correct, but not to connect.
I have tried resetting my service books and changing my email activated with my Facebook account, both of which have been suggested via other forums.
I have broadband service and can access websites, email, etc.