So, in the main quest, I am currently on the quest "The fallen". I am at the part where I need to talk to the Jarl of Whiterun to let us use the dragonreach.

I also joined the stormcloaks, and am on the quest "liberation of skyrim. I just reached the part where we invaded Whitrun and forced the jarl to surrender.

So... Now, I can not approach the Jarl of Whiterun to finish the quest "The Fallen" because he is no longer the Jarl...

Did I break my game?

There should be a new jarl. Try to talk to him his name is Vignar Grey-Mane.

I also tried that, he is not opening any dialogue options.

Have you ?

I'm not sure why it should make a difference, but you never know.

yes

Did you start a dialogue with Balgruuf and not immediately head to the balcony? I've heard a lot of people getting this quest bugged if they don't do all the steps in immediate succession.

Have you left Whiterun after the siege? If not, try leaving a few days and then come back (and don't do anything of significance in the meantime, in case you have to reload).

Or just reload an earlier save right away.