If your main router LAN iP is 192.168.0.1, then:
On the D-Link router, under Network, set the LAN IP address to 192.168.0.2. Subnet mask should match your main router (255.255.255.0). Management link = dlinkrouter. Leave local domain name blank. Disable DNS relay.
Click Advanced Settings. Disable DHCP. Under Advanced Settings, turn off UPnP and the two multicast options. Click Save.
Make sure the DHCP range on your main router does not include 192.168.0.2. You can use this IP to access the dlink router.
The D-Link router (LAN ports) cannot receive DHCP from your main router so you have to statically assign it, but it will pass DHCP data to the clients connected to the D-Link router.
Make sure your clients get a gateway IP address of 192.168.0.1 and are getting DNS server IP addresses.
EDIT: You stated earlier "Also, interestingly, when I log into the router via Firefox, it says the Internet is disconnected when clearly it is working." Are you talking about the WEB UI of the D-Link router saying it is not connected (red X)? This is correct since nothing is connected to your WAN port.