Not in the task manager tab, probably means it crashed silently
Un-install Calibre,
Reboot, just to start with a clean slate.
delete the previous download and get a fresh copy from the official site (Do Not use a download manager program).
Do a clean install.
Start Calibre (You can watch the status in the Task manager)
Do not rush to Kill the process,
some updates (I don't have a list of which releases do this) will modify the database
structure, that can take some time depending on the size of the Library. Killing that process is probably the worst thing you could do
.