How to fix Syslinux on USB booting on one machine, "no DEFAULT or UI" on another?

I have Ubuntu installed on a 2 GB USB drive with Syslinux to boot it. It works perfectly on an old WinXP-era Samsung laptop. It takes time, but it boots, shows a Syslinux menu, runs a kernel, and eventually gets to desktop state. On a significantly newer regular PC box (2012 era, 8 GB RAM, Core 2 Duo CPU or something), when it finally boots (it's finicky), it boots to say, pretty much, Syslinux (C) something; no DEFAULT or UI configuration and the boot: prompt which doesn't recognize any form of typing in a path to a vmlinuz file. So... the MBR of the USB drive boots fine, just the filesystem

Question by Sinus tentaclemonster on Super User, licensed CC BY-SA. We show a short excerpt and link to the original thread as credit.