AGAIN, READ THE POST BELOW FIRST
Likely your problem is that you are using the wireless router as a wireless router and not as a Wireless Access Point or WAP. Take the router and connect it via Ethernet to any computer. Remote into it using a browser and its default gateway (likely 192.168.1.1) and username and password (likely admin admin or admin password or whatever). You should be able to Google it. Once in it, see if there is a setting to make it a WAP thereby bypassing DHCP and firewall.
If it does not have this then try setting up DHCP to give it a separate subnet with it connect via LAN or same subnet.
Sorry for the different info. It's difficult without remoting in or being there. But, it is likely that the wireless router is giving out IPs and they are conflicting with the network IPs, plus you have a firewall, which is doing its job. Turn that off. You already have one.
When you plug the laptop directly to the Ethernet jack, make sure you either reboot to allow it to get a new IP or go to command prompt and type ipconfig /release and then ipconfig /renew. When you are connecting it to the wall, the laptop may be retaining the wrong IP settings it received from the router.
We really need to know what is giving out DHCP, default gateways, settings, etc.
