When you start the Internet@TV App, try logging in using the red "A" button on the remote. After logging in, you should see your account name in the lower left hand side of the screen noting that you're logged into the account.
From there, you should be able to launch Facebook with your account credentials. Does that help?
I just set up the Internet @ TV on my new LE40C750 today and tried adding/setting up the facebook account by;
1 - Creating an internet @ tv account
2 - Choosing the facebook connection setup
3 - Entering facebook id and password
But after pressing ok/enter it says the connection details are invalid (or some message to that effect). I've tried a few times and unhid the password to ensure I have put it in correctly and still no luck. As soon as I come onto the pc and try the same details, I log in.
Anyone else had this issue? Any idea how to resolve it? The id I'm using is a "@yahoo.co.uk" one (I'm in the UK).