Well, assuming that they're not pre-compromised, there are a few things to make this less of a problem.
First, if the hard disk manufacturer and the computer BIOS manufacturer have devised a method to password-protect the hard disk drive through the BIOS as Dell has, then passwords put on the drive are essentially unbreakable in the short-term, again, assuming that the method isn't pre-compromised. This should protect the hard disk drives from being removed and read.
Second, using filesystem encryption. Redundant to hard disk drive passwords, but in the event that the hardware drive password is compromised or somehow the kernel is crashed to allow a soft boot to another OS it would prevent a different kernel to get access to the data on the exposed drive.
Third, if I/O is secured (ie, no conventional high-speed or bi-directional hardware interfaces enabled) and if proper network security is practiced in the network interface, then there shouldn't be methods by which to compromise the computer while it's running. This may require selecting models that can still be used while secured (ie, PS/2 ports for keyboard and mouse, and no USB enabled, serial and parallel disabled) but if there are no physical interfaces that can be exploited then there are less vectors to get to the OS in a means other than by those requiring credentials.
Fourth, the OS kernel needs to be configured to not plug-and-play and newly-discovered hardware, whatever that type of hardware may be. As some motherboards can handle PCI cards being inserted without leading to an OS crash, it would be in the interests of the organization to keep the computer from recognizing or making use of any added components.
This all is contingent on the use of the computer preventing malware from being installed or on keeping an agent with credentials from getting access to it, but if users are not given too much access and if the IT department is diligent in their maintenance then it should be less of a problem. If a computer is important enough to not have a route to the public Internet or to have not have any network access what-so-ever, then it should be important enough to justify fairly considerable expense in its maintenance to ensure that it remains secure.