They CAN work, but just creating a page and expecting people to find it will leave you disappointed. If you really want it to work then you will have to promote it to a large number of friends, either people you know personally or a community you actively participate in online. Additionally, people will be more likely to donate if it's a legitimate need with proof to back it up. If your description of the cause leaves too many questions, or the personal details are just too personal, then don't expect to reach your goal.
My advice would be not to bother unless you already know a lot of caring people, or you're willing and able to fund most of it yourself. Just based on the description you've given, since it's a secret I assume you're not going to put a picture of her up there (that would help tremendously), and it sounds like there are a lot of questions you probably can't answer. Why she isn't allowed to use her home computer, for example...
That's my outlook on it anyway, for what it's worth. On other hand, maybe someone here has a spare laptop laying around and they'd be willing to hand it over no questions asked? Who knows.