I am new to Cisco software and networking in general, so I appreciate any help that the community can provide.
Here's my setup: I have a Cisco ASA firewall sitting behind a university firewall. I am able to connect to my devices using the AnyConnect VPN software. I have set the DNS servers on the cisco device to use the university's DNS servers (ie. 22.214.171.124). When I ping the ouside world (i.e. google.com) from the ASA CLI I get success. But when I ping from a server behind the firewall on a local subnet (192.168.150.0/24), it fails. The server has the DNS configured to the university IP (126.96.36.199). Is there some rule that I need to add so the DNS queries get forwarded to the right servers (sinice it's on a different subnet)?
I think you are missing a no-nat statement that was allowing you access to your servers.
access-list nonat permit ip host
nat (inside) 0 access-list nonat
Please try the above and see if that helps.