Hi Neil
The problem is occurring because HyperNext cannot find the folder My HyperNext inside the user's My Documents folder. It needs this folder for default data, projects etc. I'm guessing that for some reason HyperNext couldn't create that folder.
When HyperNext first runs in a Limited User account it should create the necessary folders and then display a First Run splash screen with info about help etc.
I've just created a new Limited user account and had no problems when running it, creating a project and running the project.
I did install HyperNext using an Admin account.
I hope this helps you pinpoint the problem.