OK, do you have any javascript blocking addons installed in FF? If no, go to your preferences under "content" and make sure that javascript is enabled.
Do you have the AdBlockPlus addon installed? If so, temporarily disable it and try again. If it works then "whitelist" all of wordpress.com (probably something like this: http://blogname.wordpress.com/*
Also, go to preferences > privacy and mak sure you have "accept cookies from sites" selected (accept third-party cookies does NOT have to be selected). And, in that same preferences window, do you have "Always clear my private data when I close FF selected? If so, it is clearing your wordpress.COM cookie out when you shut down your browser, so it is most likely losing the configuration.
Another thing to try, is just temporarily disable your virus protection software (and don't navigate to any site but wordpress while it is turned off) and try things again. Norton anti-virus has in the past has caused some issues and if I remember there were some other AV programs as well. If things work right after turning off the AV, then you will need to whitelist all of wordpress.COM.