Hi there and welcome
Can you close all programs
Open Finder and click on Go To Folder
In the window then go to Preferences
Delete the Quark Xpress folder, then restart the Mac and tell me if it then operates.
I can also do these steps for you, and have made a request via Additional Services. This is optional, and if you choose to do this, I can, with your permission, remote into your computer while you watch and do all these steps (and deal with any problems that arise during them) for you. Or if you do not choose to take this service, we can continue here. This is no problem at all. Just let me know please.
Let me know the results please