Can you clarify what you mean by "I open the project from our shared location, and it downloads the current project files to my local machine.". It almost sounds like you are using some sort of Source Control? If that's the case, perhaps your Source Control has some files locked that RoboHelp is needing in order to work.
I might be tempted to just create a new blank project and see if things work. That would ensure RoboHelp has been installed and is working properly. After that, you could then import the topics from the former project in order to create the new one.
To clarify, we have a SharePoint location that I am retrieving the files from. What you say makes sense about the possibility of the source control, it is quite possible. I wish there was an adequate error message describing that though : / I’ll have a go at creating the blank project and importing the topics in, and report back!