so to summarise:
plex works ( thus network is not blocked)
ping works ( is that on LAN or also from outside? )
maybe look in detail at how you are setting up" my first server"
are u doing anything more complex than enabling the built in calibre server, via GUI preferences ?
if you make the calibre library folders shared, can you access those OK over LAN via windows ?
Is everything on same LAN subnet i.e. all on 192.168.0... or all on 192.168.1.
double check internal library PC IP with run ipcheck
consider wiping calibre ( except for books) . reinstall then with everything on default, enable the built in server, point calibre at your books library and see what happens?
as another test, copy some books into plex ??? I know that's silly but it would be nice to confirm that the library is not totally cursed
