The symptoms look exactly like a user I had a problem with logging into my application but for them cookies were disabled, re-enabling cookies fixed it.
Firefox cookie settings are a little obscure, here is a web reference http://support.mozilla.com/en-US/kb/Websites%20say%20cookies%20are%20blocked there are 2 flags, accept and accept third party cookies. You say you have cookies enabled but I run the same configuration as you and have no trouble logging in on my applications. The fact that it works in Chrome would indicate to me that your application is in working order for the most part. Are there any Javascript errors reported?
