So, it looks like my mom's computer has a big problem, but I don't know what it is.
Here's the info: When you turn the computer on, nothing happens to the screen. More precisely, the monitor still gets no signal. The keyboard also gets no power. The computer makes no noise, such as POST beeps, and the only light on in the front is the hard drive activity light, not the power light. However, all the fans (processor and such as well as case and power supply) work. I couldn't hear whether the hard drive actually spun up, though (I don't think it did, which they usually do when you start your computer.)
I've already tried swapping power supplies, with no change at all.