Sorry she's giving you such troubles right now.
A thought - since the computer seems to be a trigger (at least superficially), what would happen if you let her have it again tonight, with the warning that it *will* be turned back over at X:00 p.m., and any argument or drama over it will result in it having to be turned back over an hour earlier tomorrow night and for the next week? Her choice - no drama and she continues to keep it until X:00, or drama and her time will be cut back. She is the one in control of it.
My initial thought was to remove the computer entirely (might be easier for you guys), but I think she's old enough to put the responsibility on her shoulders.
As far as the sleeping issues... I know it's frustrating and maddening, especially since she claims it works for her. She's probably not at a point where she can see how this is so NOT working for her. Like eating, we can't force our kids to sleep, but I think you do have to keep encouraging healthy sleep hygiene. Stay in room past X:00, read, music, whatever. I'm sure you've done this already, but ... I think you have to keep on keeping on with- it. Hopefully as her depression is treated, she will be more receptive. I don't think it's that she doesn't want to get better - depression is just such a horrible vicious cycle that once you're in the very darkest depths of it, it is *really* difficult to climb back out. It will take time.
I agree with- not trying to stop her from bolting. Let her know up front what the consequences will be, and again put it on her shoulders.
What are you doing to take care of you right now? You are really in the trenches, but you have got to remember to recharge your own batteries so that you can keep on dealing with- this.
Gentle hugs to you.