Update:
After trying to update from the Intel Chipset to an ATI Radeon card, we still had the same issue--Windows was unaware of the the display hardware's status:
Highlights:
Card name: ATI Radeon HD 3400 Series
Manufacturer: ATI Technologies Inc.
Chip type: ATI Radeon Graphics Processor (0x95C5)
Display Memory: n/a
Video Accel:
DDraw Status: Not Available
D3D Status: Not Available
AGP Status: Not Available
It was clear that we would need Windows to know that DirectX was installed and
operating properly. We found a prior thread (also dealing with Optiplex systems) where a user describes a solution they found for this issue:
http://www.empirisoft.com/Support/showthread.php?p=9407
We followed to the instructions to change the registry key to "7" instead of "0" and after a reboot, the system recognized all the required DirectX components and DirectRT was able to start. Tomorrow, the lab will test the machines to see if their experiments can run now.
See also: http://support.microsoft.com/kb/191660