set the program to start on boot, set the computer to log in a user on boot, set the computer to not complain when no keyboard found. Turn off computer, remove keyboard and mouse and disable the ports (non-conductive silicon putty would do with a layer of superglue on top). Turn on computer.
How can I get a computer to run one program and only one program?
What kind of program do you mean? Isn't operating system a set of programs, system services, device drivers, kernel, etc?
If it's a Java based program, does not it take a JVM (which is a program itself) to run it?
What does your program do? Does it have GUI? Does it interact with an operator at all? How does it make results of its work available to anyone? Is it configurable? How do you plan to interact with it if it's the only program running at this machine?
in windows 2000 it is pretty easy to make it so they can only run one program. just set the ntfs permissions to only let users run that one program. furthermore, you can set up their profile so that is the only thing they even see. as far as the browser question, i dont know.