Okay, so here are my theories, and I want someone to correct me if I'm wrong because I really do want to know how this works in case people ask why I'm suggesting they do a power cycle. My theories are:
Removing all power from the system, minus the 3 V battery powering the CMOS, causes one or two of the following to happen:
A. The BIOS resets because ~3 V is not enough power to maintain it.
B. The BIOS and CMOS chip are designed to reset if less than say 3.5 V are powering them
C. The rest of the system is completely devoid of power, so there is a hardware reset in the sense that no
components are able to run, and so no power memory remains in components to cause them to continue
working incorrectly. Thus, when the computer is given power again, components not powered by the 3 V battery
are reset to their original working condition.
Edit: I looked into this a little more, and I'm wondering now if this might be due to RAM being corrupted, and a simple power cycle (turning off the computer, waiting 10 seconds) does not clear the RAM as completely as removing all power and doing a full power cycle.