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?