I know that this is an old thread, but when I had this problem (old favicon) what worked for me in Moodle 1.9 was:
1- With your browser, navigate to the address where the new favicon is: Ex: http://mydomain.com/moodle/theme/formal_white/favicon.ico.
2- Probably the old favicon will be showed. Then press CTRL+F5. Now the new one should be seen. If not, the address is not correct.
3- Now open Moodle and probably the new favicon will take place. If nothing happens, then you should check if favicon is in the right place.