You're friends not alone with this enigma - I've got the same problem on my PC.
I'm using version 4.0 (Passport) and the overlaying fonts list stops at Nimbus SansT. No font beyond that is available and I usually have to find a similar font in the list using the font folder similarity facility when I need to use something like Times New Roman. It's so annoying.
I've spent years looking on the web for an explanation and have found nothing conclusive. I've read that it could be caused by Quark having a limit on the number of usable fonts, but I've not discovered what the figure is supposed to be. All the same, it might explain my problem as my fonts folder contains about 1200 fonts thanks to all the Adobe stuff, Quark and the usual Microsoft software.
I've tried creating a new fonts folder with a limited number of fonts to see if that made a difference. It did not.
Quark does take the fonts from the fonts folder in windows and I never read of the need to install them anywhere else on the PC or change the attributes of such a folder.
If you find the answer, let me know!