Ah well now we're getting somewhere!
So you can ping between subnets in both directions. This implies pfSense is correctly routing packets and that the firewall is not blocking traffic, locally at least. If it were blocking due to the default rule it would show in the firewall logs.
What is the result of attempting to ping, say, google.com from the server?
The problem is either no dns service or no route to 'the internet'.
Possibly the DHCP server on LAN2 not giving the correct value or NAT not working correctly (it's definitely not set to manual?).
Alternatively the "No Internet Connection" warning could be incorrect for some other bizarre reason.