So i want to try SC2 demo before i buy the full version, because im not sure can my computer run it.

I tried to download it from here: https://us.battle.net/account/sc2-demo.html
It says "You are now ready to play StarCraft II!", and when i hit the Download button, it just opens an empty
page and says File not found.

I've tried this with 2 different browsers ( Firefox and IE ). What could be the problem?

That file isn't available and no localization exists for it. What language are you using from the website dropdown menu? We're not finding anything that exists or links that file.