If you cant dig google.com @8.8.8.8, which doesnt involve Pi-hole, it sounds like your router is blocking DNS queries.
You mention the router has changed.
Check for below or similar security setting on the new router:
EDIT: try do a DNS query on the Pi-hole system that Pi-hole knows about and doesnt need to be forwarded to an upstream DNS server like Google's 8.8.8.8.
Eg.