Sorry to burst your bubble Plum, but Hero was already nominated for Best Foreign Film back in 2002. The reason why it took so long for it to be released in the States was because Harvey Weinstein didn't feel like releasing it (not even on DVD) after he bought the American rights to it. It wasn't until Quentin Taratino, fresh off of Kill Bill success, finally got Harvey to do a theatrical release.
Since it was already nominated for Best Foreign Film, the rules state that it is no longer eligible for other awards too. So unlike City of God where it failed to get nominated for Best Foreign Film in 2002, but was able to get nominated for Best Cinematography, Best Screenplay, Best Editing, and Best Director in 2003.
The rules are a bit weird for foreign films. If they are just submitted but not released theatrically in the U.S, then they are still eligible for Best Foreign Film (but no other category)if their host country(only one allowed her country) wishes to submit that film that year if they play in L.A. for 2-3 days. If they fail to get nominated for Best Foreign Film, but they do a wide theatrical (wide meaning limited too, I think) then they are still eligible to get nominated for other categories if they wish to do so. If they were nominated, they can't.
Some movies like Life is Beautiful and Crouching Tiger, Hidden Dragon lucked out because they were widely released in the same year they were eligible for Best Foreign Film. Therefore could get nominated for all the categories including Foreign Film.
Of course, my citation of the rules are a bit iffy. You're best bet is to check out Oscar.org and read them yourself.
"I've got to get me out of here
This place is full of dirty old men
And the navigators and their mappy maps
And moldy heads and pissing on sugar cubes
While you stare at your books."