My car has failed to start several times. Shops can figure it out.

70,000 miles. The head gasket was leaking, but I had that fixed. This has happened several times over the past couple years. I don't drive the car much as I live close to work, so have been told that drains the battery. However, I've replaced the battery and it still happened shortly after. Also, if the battery was low, the car shouldn't simply start when we keep trying, or let it sit half an hour and then try.

You can either leave it at a shop long enough for them to duplicate the problem, or just have the starter replaced. My guess is that is the problem. If you can leave it at my shop for several days I will try to confirm that, and still only charge the minimum diagnostic charge, however, depending on the frequency of the issue it may be hard to confirm. Next time it happens try to verify the "clicking" sound. If you do here a click then the starter and or connection to it are the problem.