Now the computer won't boot. The fans start to spin, the hard drive
begins to churn and then, suddenly, there is a click and the the hard
drives go quiet and then start spinning again, and then there is a
click, etc.

On the front of the computer, the green light turns on, as does the
DVD drive light, but then the lights turn off momentarily when I hear
the click.

Is this clearly a power problem? Do I need to bring it to be repaired?