Thanks for the reply, piete. Here's what I've discovered, which I'm also posting for the sake of anyone that might google up this thread in the future.
A little more research seemed to confirm that the error message I receive is related to acpi. For example, the message is quite similar to the following:
http://bugme.osdl.org/show_bug.cgi?id=2665
Although that bug report is marked closed with a code fix for kernels after a 2.6.6 release candidate version, finding it confirmed my hypothesis that it would be useful to try recompiling a 2.6.11.11 kernel without acpi.
So I did. I don't have another system I can compile on, so I took a whole lot of things out of the config in order to try to speed up the compile as much as possible, which means that I might have introduced some additional problems. In any case, the new kernel without acpi support still would not boot and gave the same error.
However, I think there may be another explanation that does not concern acpi. My laptop, the Compaq Presario 1230, has an unusual processor, the Cyrix MediaGX, which is classified as i586 with MMX. The processor uses the Cyrix 5220 IDE controller. Now, in the kernel config menu, support for this particular controller is marked "VERY EXPERIMENTAL" (with the caps, too

).
I think my non-booting kernel just may demonstrate the reason for this. In booting (both with and without acpi support in the kernel), the 5220 IDE controller is recognized. The boot hangs just afterward, during detection of the IDE cd-rom.
So my conclusion is that this controller isn't working yet in the 2.6 kernel, which also explains why I've never successfully booted any version of the 2.6 kernel on the machine. There isn't really enough evidence to know for sure, but it seems a likely explanation to me.
Maybe someone is working on this, even though it's old and obsolete equipment (that nevertheless can do a lot still). I haven't yet discovered whether my feedback could be useful, and if so how to go about sharing it, but I've only googled a little at this point.
Anyway, I hope this information will help out anyone who might encounter it. The 2.4.31 kernel in slackware-current runs just fine, BTW, and that's what I'll be sticking with for the moment. (Although I might compile a pared-down version while I still have all the tools to do so installed...)