[kovidgoyal]

I doubt it is video card drivers, that would not explain the difference between cold and warm starts.

To me at least the issue seems obvious:

1) It is disk access related -> implied by difference between cold and warm starts
2) Something on the problem computers is greatly slowing down disk access to the files specifically in the calibre program folder (there may be files in other locations involved as well, for instance the calibre config directory or various places in the OS that Qt might scan)
3) Whatever that something is, it has system wide effects. Therefore, it must either be a disk driver or something that interferes directly with the kernel -- the most common such program is security/antivirus.

However, trying to find out what the problem component on the system requires a level of familiarity with window's internals greater than I posses.

EDIT: Of course, computers a very complex machines, and it could be that it is a combination of several factors. For instance, the difference in speed of loading DLLs between cold and warm starts could be triggerring a timing related bug in some unrelated driver, like the video driver. But, that kind of thing would require pretty heavy instrumentation to debug.