I was fighting similar issue years ago with a Microsoft Visual Foxpro application that I wrote for a company.
On some computers it took a long time to start the application and/or do certain operations.
That was a big deal, because the issue was wasting valuable employee time.
I ended up installing something like this:
http://www.nirsoft.net/utils/opened_files_view.html
that enabled me to dump and analyze every single access to a file or a directory - to see what the program was trying to access.
I was shocked to see thousands of file [directory] access handles as the application was searching the $PATH and system directories for for an executable file, dll libraries and hundreds of things a modern application needs to run.
I would suspect that something is trying to access some network share or something that doesn't exist. There is similar problem when running older versions of MSOffice when some network shares aren't accessible and you try to do some unusual stuff, such as opening "SaveAs" or "Open file" dialog panel ;-).
I suggest installing a piece of software that can logg *all* file acess, rebooting a machine, waiting a bit until things settle down (and all programs that need to do stuff upon startup finish the work), then activating the logging and starting Calibre.
As a next step you can try to run some process explorer software (even the windows built-in one) and watch what software / library / service is most active during the 30 seconds when Calibre freezes the computer.
I also like to install "startup guard" plugin to Total Commander an weed out all software that is scheduled to start automatically after boot. *Everybody* (*) and his brother think that their little piece of software is the most important one and they try to start it behind your back, so it is ready as soon as you want to use it, even if you need to run it four times a year - for things like backing-up your contacts from your Nokia dumbphone. If they do not start the software itself, they will at least try to check for updates or preload something. Sigh ... .
Startup Guard lists all programs that are set up to start automatically (not services) and you can disable them by a simple doubleclick. I like to disable everything - the three system programs that do need to be started automatically will add themselves to the startup somewhere again. When in doubt, disable the software and then when you miss something you can re-enable it again. You might want to let the Antivirus run ;-).
And while I talk about my beloved TotalCommander, there are quite a few plugins, one of them process explorer that will let you see what is running on your computer. There are quite a few processes started by default that you can safely disable [at home].
One of reasons I prefer to use something other than Windows at home is that I do not need to run antivirus that needs to check every single file before it is accessed by any application.
(*) Calibre is one of notable exceptions. Thank you Kovid ;-)