I have a niece; her mom tried hard to get her interested in piano but made no progress. At the farm one Xmas, I was upstairs practicing the Bach 'Chaconne' on violin. The niece came up and watched. I put my violin under her left chin, showed her how to hold the bow, and she made a sound.
The next day her father asked me, "How much is a violin going to cost me?".
Lesson: Children can get more interested in activities they see adults interested in and liking.
The difference: The girl's mother didn't like piano enough to play it. I really like violin and was working hard playing and practicing it. The Bach 'Chaconne' is not a trivial piece of music, and it's possible to get really involved in it, which I did. Those are all big points.
So, for a girl and computing, first, interrupt some of your hard work at you computer, sit her down next to you, and show her how to do some things. E.g., show her how to type "Hello World" into some word processing program and print it. Show her how to use a Web browser and e-mail. See what else she is interested in, and help her with that.
Eventually get her father to buy her a computer. I suggest a desktop computer in a mid-tower case, with your help, she can assemble herself. Likely install both Windows and Linux.
Get her started on programming, say, in some interpretive language, maybe Python.
Get her a project she would like to do, maybe build her own Web site and use her computer as a Web server.
Get her well into word processing so that she can do better with school term papers and, more generally, practice her writing.
Learning to read in some data, analyze it, and plot it stands to be good for her when she gets into high school math and science.
I have a special suggestion: Get her a really good editor, one with a good macro language. I use KEdit. Except for Web browsing, I by far my most heavily used program is that text editor; I use it for a huge range of things. Good skills with a good text editor are darned good to have.
Take it from there, and, say, report back on what did/didn't work!