First question - no, there aren't a lot of women in computing, whether its programming or maintaining computers. However, as a woman, you probably will find it easier to get hired because of this.
A computer science degree really has nothing to do with maintaining computers. A CS degree is all about how to program and design software. There is a lot of math involved, because you need to understand things like how to sort an array of potentially billions of numbers in the most efficient way. Stuff like that.
If programming interests you, then yes, a CS degree is the way to go. But what you are describing would be the role of a system administrator rather than a programmer or software engineer. If you want to be the person who maintains the computers(and possibly the networks) in a company, then an IT(information technology) degree may be more suited to you. You can pick up an IT degree at a community college or something like ITT in a couple of years, and its geared a lot more toward becoming a system administrator.
Sometimes you will see a system administrator job that asks for a CS degree, but they almost always say "or equivalent experience" in the job description. In my experience, very few CS majors actually want to become system administrators. I did have an elective in my CS degree program that covered Unix system administration. I did a presentation in that class and asked how many people wanted to go into system administration. No one raised their hand. All of us were taking that class for the easy A, and were there in the degree to become programmers rather than administrators.
Thats not to discourage you from taking CS, but IT is a lot easier, it takes less time to get your degree and get employed, and if you find out you want to get a CS degree down the road, IT is a pretty good background for that.