On Firefox you click onto Files, then import. You can import all your favourites from IE to Firefox. If you want to save new sites just click on Bookmarks which you will find at the top.

When I switched to Firefox I was asked by the programm after installation if I want to transfer all bookmarks (I used Microsoft Explorer before).
Of course I did and it worked fine.
But tonight I thought of another probably cause of your problem. Did you install a new firewall/ anti-virus program?
Some of them refuse any downloads, you have to allow exceptions.