I decided to try to install 10.2 on an older machine (450 megahertz Pentium II, 384 megabytes of RAM) at about 7 years old (but it still performs very admirably). It installed fine, and I'm very impressed with it when it actually boots. About 50 percent of the time, LILO seems to initiate it okay, but after LILO finishes it then errs out to a blank sceen. Nothing happens. About 25 percent of the time, LILO finishes, but my system strangly reboots immediately afterwards. Note that I have never had this problem with another Linux distribution, excluding Vector Linux (which gave me the exact same issue) which is interestingly based on Slackware.

I'm a bit stumped, but if you think it might be acpi - you can turn it off from lilo.

http://tldp.org/HOWTO/LILO-9.html

The link is obviously not a direct solution, but shows you where to add `append "acpi=off"` to your lilo.conf. Presumably this can also be added at the lilo prompt, too.

Have you tried checking you bios? Tinkering with stuff in there can sometimes help - also check your RAM with memcheck or similar, see if that helps.

What was the difference between the other distros and Vector/Slack? I know SuSE uses grub - might be as simple as the configuration of lilo is not optimal.

Sorry I couldn't be more help - good luck,
- Piete.

If it boots properly ever, it doesn't seem like a configuration issue. I would suspect bad RAM, bad HD, etc., on such an old machine before checking anything else, given what we have read.

I'll try turning ACPI off; other than that I'll just keep looking for a solution. I highly, highly doubt that it is the RAM or the hard drive. Number one, I upgraded everything on the computer but the motherboard and the processor last year. All of those components are new. Number two, every single application, and every other operating system, has worked as it is supposed to on this computer, until Slackware.
I'm reaching here, but perhaps it is an issue with the older (2.4.31) kernel I have installed?

That's the default Slackware kernel, and it works. I haven't seen any other reports of this problem, so I still believe it's a hardware issue.