If your syslog input fails to start it’s probably because the graylog-server service is attempting to bind to a priveleged UDP port (514 < 1024).
If your system uses systemd as the init system (most these days), then there’s a very clean fix.
You need to find and edit the systemd unit file, which will named graylog-server.service.
vi /usr/lib/systemd/system/graylog-server.service
Add these lines to the [Service] section:
# allow binding to 514
AmbientCapabilities=CAP_NET_BIND_SERVICE
Then reload the server:
systemctl reload graylog-server
Inputs should start automatically.