Here in the UK things are much the same as it is for you guys in the states. In Cambridge where I live there are hundreds of people that can fix computers, so I have to keep my prices at a low level.
For the last couple of years I've charged a set fee of around £45 plus parts (about $60) for whatever I do. My customers fall mainly into two catogory's. They're either very poor and would not be able to afford the large store prices, or they are elderly people who especially need to be able to trust people who come into their homes to provide a service. Both of these groups of people tend to tell their friends and neighbours about me. I may not see some of my customers more than once or twice a year, but I do get to meet their friends and neighbours.
In addition to fixing a customers problem, I also try to spend some time giving advice on what I consider to be good practice. Maybe showing them how to use Word, or how to make a music CD for the car, etc,etc. Customers also often say that they've been told by a friend that it's possible to get a paid for program or piece of software for free, and could I do that for them. Of course I have to explain to them that what they are asking of me is illegal, and although I am not able to do that myself, that there are people on the internet who will happily give them advice should they choose to go down that path. That's always a tricky situation to be in, but I take the view that I am not their moral keeper.
I should point out that in addition to my computer repair work, I am fortunate enough to have another job as a rent collector. Without this, I'd find it difficult to manage just doing PC repairs!
Sometimes it is possible to offer your service too cheaply. As has already been pointed out, people may believe that you're not offering a proper or professional service when you're cheap. I suppose that it's just a case of striking the right balance.