I really would just like some people's opinions on this, because the more I think about it, the more I'm pissed off.

I stayed at my boyfriend's house a few nights ago, and I brought over my laptop. We used it to watch videos, play games, check Facebook, etc., until late at night. Since there was nowhere else to put it, I placed it on the floor near the foot of the bed, out of the way of the general space of the room, before I went to sleep. The next day I turned it on and found the screen to be cracked and completely destroyed. It turns out that his mother had stepped on it when she woke him up that morning and went to turn on his closet light. I could not have guessed she would turn on his closet light on the other side of the room, when there is a lamp and the overhead light switch within an arm's distance of the door, which I had only ever known her to wake him up from. She also was very aware that I had the laptop at their house that day, because we/I had used it while in the same room as her for an extended period of time that day.

Now, I understand that it was an accident, and that's fine, but I believe she should pay for it to be fixed. She, however, believes that it was my fault that it was on the floor, and therefore has only offered to pay for half of the repair cost.

Please also consider the fact that she is a working adult with savings and income. I am a full-time student with no savings or income; the laptop was a graduation present from my family.

What do you think? Can I ask her to pay for the full repair? Who is at fault?

At least she has (I assume) admitted to being at fault,rather than saying that you may have dropped it, etc.
What was the problem with putting it under the bed?
Frankly, I'm surprised that she has offered to pay half-I would pay nothing toward the repair if I had stepped on it in that situation.
And if it's a Dell, send her a Mother's Day card..she's really doing you a big favour.

She would only be responsible for paying if she was at fault. If nobody's at fault, the cost should ultimately fall on you, as it is your property and your responsibility to keep it protected.
Lets look at the situation from her perspective. It is true that she knew you had the computer at her house. But, she has every right to assume that you would not leave the computer on the floor. You can say that there was nowhere else to put it, but lets be honest, you can always find space somewhere if you need to. If you can't find space, make it by putting something that isn't worth so much onto the floor. Secondly, it is not her responsibility to watch where she's stepping, especially in her own home in the dark. Your taking advantage of her hospitality if you think otherwise.
You made assumptions about her actions (such as which light she was going to use in the morning) and you were wrong. Your incorrect assumptions ultimately are your responsibility, in addition to the consequences that follow.
Let me put it this way. She is being overly generous by offering to pay half. If you ask her to pay it all, you will likely lose all respect from this woman. In addition, she may be taken aback by your ungratefulness and refuse to pay anything at all. Asking for more money is just not worth the risk (nor is it justified). Rather, take what she offers, thank her, and learn from your mistake.

Matt sums it up fairly well.

I find your additional information that you threw in to help us decide a bit troubling.

So this woman works and you are a student and this was a gift. Why should this have any bearing on the case.

A corrolary to it might be the dole. The working taxpayer funded it and it was given to you, and now you expect them to foot the bill for the repair due to your carelessness. And if they don't pay again you won't respect them.

The fact that this woman is offering to pay half is very generous. If you have to work to return the item to functional status perhaps you will take better care of it next time as you now have sweat equity invested in it.