While you have a name server specified for the router itself, you aren't providing DNS server information to your DHCP pools. Do the following (assuming that you want the pools to use the same name servers as in your configuration for the device itself):
ip dhcp pool "LAN"
network 192.168.1.0 255.255.255.0
dns-server 188.8.131.52 184.108.40.206
You'll need to have the DHCP devices release and renew their connections to pick up the change.
Huh, that's what I figured, but when I would set DNS in the GUI under DHCP Server Pool "LAN" -> Optional Settings, clients could resolve DNS for a short period of time, then they would stop, and when I checked back at DNS under "optional settings" the DNS entries would be blanked out. Is this a bug in the GUI? Or am I missing something?
It could be a bug, but this is unlikely as it would affect others and there would be reports of it. Entering nameservers into DHCP pools is a very common configuration and such a bug would bring a lot of attention.
Perhaps the configuration was not saved? I would try to enter it into the CLI, then write to memory and reboot to see if it sticks.
It could also be malicious. Looking at your configuration, telnet access is enabled with default password. I'd recommend disabling telnet completely and also make sure to remove the "admin" user from the default configuration.