Your passwords are stored in Signons3.txt, and encrypted with a key stored in key3.db (in the same folder as Billy said).
If you copy both (and you need both) those files into your new profile (%APPDATA%\Mozilla\Firefox\Profile\[random text].[profile name], you should be able to access all the saved passwords.
It might be called signons2.txt/key2.db, the same principle applies.