You said you were able to ping Pi-hole after the switch but were unable to do DNS lookups against it.
Were you able to SSH into the PI after the switch ?
Flipping on the Pi-hole DHCP service should not alter any of the IP details for Pi-hole.
It could be that your router does something like below:
I can see this settings in your router "Enable DNS relay", not sure what that one does but you could try disabling it (for diagnosing) ?
You could also try connecting a CAT5 cable straight from Pi-hole to one of your clients.
See if the client receives an IP address from Pi-hole and try to do the lookup again with the router out of the loop.