I am a woman, thank you! And my name isn't Norton!
Anyway, so last night I again attempted to troubleshoot my computer. First, I cleaned a massive amount of dust out of the computer, including wiping the video card and the fans.
The monitor failed to turn on again and again, and I tried to turn off the computer, but it kept restarting of its own accord. Finally, I somehow got it to a black screen that allowed me to choose safe mode. Once in safe mode, I tinkered around with some of the fixes I've seen on the Internet and on here, including checking for disk errors (it told me I would have to restart Windows to do that, which I was hesitant to do).
Again, while in safe mode, the computer restarted by itself. Miraculously, it ended up going to the normal mode just fine, where I ran my anti-virus. Halfway through, the computer restarted. Again, it went into normal mode, I reran the anti-virus scan, completed it (it found two potential problems in some sort of Windows restore file?), and then turned the computer off normally. I have not restarted it since.
I have not seen that countdown box again. Now, it sounds like a power supply problem as y'all have suggested, or maybe a RAM failure.
More thoughts? It seems cleaning the dust allowed me to at least get to normal mode; now I just have to combat its tendency to restart itself.