No it is not normal.
What type of internet connection do you have? if dial-up it may be that the download is taking all your bandwidth.
What happens when you try to access any web site? What error messages do you get?
I just started to use Firefox. While I download any program(only one download at a time)I can't acces any site until the download is completed.Is this normal with Firefox or is a setting I should do ? I use win xp home SP1.