How can disconnecting the battery from a laptop fix malfunctions?

I'd like a technical explanation of a fix I've seen for some HP laptops.

The user turns on their machine only to find a blank screen; the screen doesn't even turn on, but all of the keyboard LEDs and the fan are running. The computer becomes very hot. I fixed this on my laptop after finding an answer here: unplug the laptop, take out the battery, hold down the power button for about 30 seconds, plug the laptop in (but not the battery), and turn it on. Another friend of mine always has to leave the battery out for the laptop to start.

I'd like to know how this sort of thing is possible. Did something in the circuitry break or melt? Is there a logic error in the design?

This happens if the capacitors on the board are overcharged; it's either a safety mechanism (to prevent overvolting, some motherboards do this) or simply a malfunction from the extra electricity. The act of attemping to power on the machine without a power source drains the capacitors, and voila - functioning laptop. There can be a lot of causes for this - static electricity, ambient humidity, unstable/dirty power source, problems with the battery, or even a problem with the motherboard itself. It shouldn't happen with any regularity unless there's a component problem, or alternatively you make your living doing belly slides on shag carpeting.

Note that this can happen, not just on laptops, but on desktop PCs as well. Beyond that, it can happen to pretty much any sufficiently sophisticated modern electronic device, in theory. Laptops are just especially susceptible due to their design, so it's generally the only place you see this behavior.

The problem is that the laptop has crashed. Typically, some piece of hardware gets into an inconsistent or locked-up state, usually the part of the motherboard chipset that controls power sequencing itself. Because the power sequencer runs off standby power (otherwise, you couldn't turn the computer on unless it was already on), simply turning the power off isn't enough.

Removing the battery would eventually solve the problem, as all power would eventually deplete. But the laptop was never designed to drop its standby power all the way to zero as that's not supposed to happen under any normal operating conditions. To force it, you have to try to power the laptop on. That will drain all residual power from everything but the circuity that sustains the CMOS clock and BIOS setup information, which will unfreeze the laptop.