So port range is something often found when it comes to programs opening connections during operation of the program. You can check this with for example sysctl net.ipv4.ip_local_port_range.
But when it comes to the ports you use as an active port when you start the program this is up to you. The kernel space for ports is from 0 to 2¹⁶=65536.
So from your feedback that it did not work to try range 8000 I am wondering more specifics here. Did you try to set this port when you ran the cardano-node with --port 8000 ? If so is this maybe a firewall issue did you have that port open to either specific ips if you could or if a public relay opened up that port to the world?
Also keep in mind that others ports are written in the topology configuration file and these ports you do not change since you would then not be able to reach those peers if you changed ports to something else. So if you mean to change others ports then obviously do not do that.