Is there any way to impose absolute, guaranteed physical security?
Unfortunately, no. Any door can be kicked down, given a sufficient amount of force, and any cable can be cut with sufficiently large cable cutters. The idea, however, is to make the criminal's job as difficult as possible and to prevent non-criminals from accidentally interrupting your service.
My CD-ROM drive doesn't have the capability to disable only the eject button, but it can disable the eject function altogether. Can this work?
Yes and no. If you never need to use more than one CD, power up the drive, insert the CD, disable eject, reinstall the drive, and you're good to go. However, if you simply disable eject completely on an empty drive, why not remove the drive entirely, thereby both removing temptation and saving electricity?
Are there any more secure ways to allow for publicly accessible machines?
Yes! If the application you need to provide is text based, consider purchasing a dumb serial terminal to run the application. These are often very inexpensive and can be configured easily with Linux using a serial port. If you need to provide access to graphics (X11), consider either building your own inexpensive X-terminal using an old PC, Linux, and XFree86 or even purchasing an X-terminal from a Unix hardware vendor. In either case, your important data can stay sequestered physically in another secure room.
I use Linux at home and am primarily concerned about Internet security. Does this hour apply to me in any way?
It may, though some of it is already true in the home context. Obviously, you want to know who comes in to your home at all times. Still, some modifications, such as disconnecting the reset switch and investing in a continuous power system, can prevent unwanted accidents that might otherwise result in data loss. If you plan to run a server of any kind in your home, these issues are important as well, especially if you have young children around who might be tempted to play with the server system.