Quark need some files from VisualC++ 9: winetricks vcrun2008. This gives you the files mfc90u.dll, msvcr90.dll and msvcm90.dll. Only to know whats happens behind your back.
Quark also needs the original GDI+: winetricks gdiplus. The related file is gdiplus.dll
run wineboot -f -u again. (facultative)
Download the installation file from Quarks webpage and start the installer.
Start Quark with wine /path/to/QuarkXPress Passport.exe
Due GDI+ is still under construction you will have to check every new snapshot, if the workaround with winetricks gdiplus is still necessary.
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From a comment here in the AppDB: Quark with Ubuntu by Odin on Monday September 6th 2010, 14:01
To put pressure on the Quark team to make a version for Ubuntu, go and tell them the need for it in this thread: