By reporting immediately, did you go to the handling staff BEFORE clearing customs, otherwise if they have not seen it and filled you out a damage form at the time, then you are going to have problems, as it is harder for them to verify what happened. I do not have the number to hand for claims for baggage damage, but it is not based in their headquarters so chances are that it may not have found its way to them. Get in contact with those at the airport at which you arrived and start from scratch. Make sure you have all evidence of travel etc. They won't be trying to avoid you, but patience may be needed still.
I was informed when I had damaged baggage that it would take at the very minimum 4-6 weeks to process (1 month ago), so 2 months is not really that much longer than they advertised.