There may be a packet filter rule blocking DNS...check to see fi this exists, or ensure you are using the UTM LAN address as the DNS server.
I can't explain why some hosts work and others dont at this stage.
Are all hosts using the correct gateway ?
DHCP server is setup correctly for the new 565 install ?
I assume wired clients, not wireless are having trouble ?
diagnostics -> packet capture
can be useful.
-s 1500 ip proto 1
will capture all ping requets and replies.
See if there is a difference between hosts that work and hosts that do not.
Hope this helps.