This issue is due to a problem with ATI/AMD graphics drivers and can be an issue for multiple programs as well as ConQuest.
The solution is to disable the ATI/AMD graphics driver in the remote dektop while using ConQuest as follows:
1. Start device manager (type that in the windows menu).
2. Find the Display Adaptors section and locate your graphics card - it will likely be an AMD device of some type (e.g. radeon).
3. Right click on the ATI/AMD device and select 'Disable Device'.
ConQuest should now start normally.
We would recommend repeating the process and selecting 'Enable Device' after completing use of ConQuest as while disabled the display generated on the remote system will be inactive.