This was an older Biostar M5ATA motherboard with an AMD K6/266 processor. Invariably, in hung at the following spot during the boot process:

Building DMI Pool
Verifying DMI Pool Data....

A description of this problem (although specific to another manufacturer's motherboard) gave a hint: perhaps the BIOS was corrupt. Flashing the BIOS was not an option, since the system never reached the point where it could boot from a floppy containing the Award Flash program. I attempted to reprogram the BIOS chip using a PROM programmer, but it reported a chip failure. So I replaced the chip (a 28F1000P Flash EPROM) with a compatible UV-erasable PROM (27C1001), which I programmed with the latest BIOS update. The motherboard then booted correctly.