Alright, that IS a very old computer, from 2007 and even then they though it was out of date:
http://www.pcmag.com/article2/0,2817,2189791,00.asp
BUT, my company provided work computer is also from 2007 and for MS Office and Websurfing it IS still functional....
Most likely problem is the Facebook, like web browsers, anti-virus programs, and OS patches always seem to heap more work onto your system. This will slow things down, nothing wrong with the computer, you just can no longer run the application (Facebook in this case) with what you have. Things move forward...
Adding more system RAM might help..... (I had 2Gb they "upgraded" me to 3Gb on work computer, it made a world of difference)
BUT, I would first try loading Chrome (instead of FireFox) for your internet browser. I've heard it is lighter on resources and faster than FireFox...) This might help you out....