FWIW, it's possible to boot the Linux kernel in about 4-5 seconds without TOO much effort stripping it down. 10 seconds is readily achievable; you can probably even to do it on a distro stock kernel if you're careful about what gets thrown in the initrd.
The X server starts in about another 2-3, generally, and a tiny window manager like lightbox, twm, fvwm, etc. is almost instantaneous these days. It's the "desktop environments" and whatnot that take ages to start, as well as starting all the services and whatnot that you don't really need on a system like this. The embedded guys frequently try to get total system boot time (including bootloader, etc.) under 10 seconds, and many people go for under 5.
You won't do it with a stock desktop install of Ubuntu, mind you, but it's quite doable, and you get a lot more facilities for your trouble in terms of modern hardware support than you do with DOS. If you know what you're doing, I'm not sure it's even that much more of a hassle.
An SSD or CF/SD card for your storage will help. At those boot times, the time spent in the BIOS startup screens is probably a significant part of your boot time.
Actually doing it is left as an exercise to the reader...
(It's actually also possible to get pretty close with Windows, these days, but doing so is a real pain in the butt, and some of the tools you need are either not public or not really supposed to be public)
Also, you'd laugh at the boot time of some modern arcade games. While some of the old ROM based games with no startup checks were essentially instantly playable, I clocked a modern title at over 12 minutes, recently.