You should save, right next to her, before trying to wake her up. Make a hard save. As soon as you try, Barrows will speak to you, and for him to wake her up for you, you need to pass a speech check. And if you have a low speech skill.... A previous character reloaded over 30 times to pass that speech check will a skill level of about 25. There's a ton of ammo in that box.
If she doesn't wake up and you don't pass the speech check, you will never open it. Spoiler about how I usually handle the end of that quest in previous characters:
Spoiler
I give everyone ammo except Brick. That way, when she dies, I get arguably the best armor in the game, stat-wise, and a unique mini gun that does nearly double damage over normal ones, and is more accurate.