Have you tried changing your port like many others have suggested? Pick something relatively high, like 45000 or so. 8080, 8888, 8088, etc are all pretty common ports and I bet your antivirus is blocking them separate from your firewall because of that. However apps still need to be able to open ports, and oftentimes higher port ranges are allowed.
Then again, it could be that your AV is blocking any listening processes (aka, servers) rather than ports, so you might just be out of luck. Though you can't turn off your AV, is there no way you could modify its configuration for example to allow the calibre-server.exe process?