Of course not, because these media were stored on your old computer. Adding media into a Plex library does not upload them into a kind of cloud storage.
Did you “claim” your newly installed server (i.e. connected it with your plex.tv user account)?
See New Claiming Requirement for Windows
When your web browser is asking you, whether app.plex.tv is allowed to access your local network, you need to say “Yes”.
https://forums.plex.tv/t/important-note-about-the-plex-web-app-local-network-access/933264/1
