I have been looking through the FDTI site and I may have identified my problem. There are two types of drivers for the chip on the Techzone board - VCP drivers and D2XX drivers. The VCP drivers set up a virtual COM port and those are the ones that I installed. The D2XX drivers allow the software to access the USB connection directly using a DLL.
It seems possible that I should have been using the D2XX drivers instead of the VCP ones that I installed on my workstation. It is certainly worth a try anyway. I will install the other set of drivers tonight and see what happens.