i just upgraded to firefox from firebird .8. i love it. i always use the mouse gestures extension so i can simply hold down right mouse button and move my mouse around the screen to have it to things. tabbed browsing = $. saving tab session and restoring it in a browser crash = $.
i am positive that you dont connect to the internet through IE. you connect through something else that probably automatically launches IE and is probably set up to close the internet connection when IE is closed.