So you have an ISP provided device, which is capable of DHCP but under normal circumstances you have DHCP disabled on that device is that correct?
Then I assume that you then plug that device into the WAN port on your wireless router that has DHCP enabled and that is providing the .2 network resolution to the rest of the computers on your network is that correct?
When you do this can you tell me what the WAN address is on the router, I don't need to know the exact ip address just trying to determine if it receives a public address from the ISP device or is it getting a .1 private address and the computers are getting addresses that are double natted.
In either case maybe try disabling ipV6 in the properties of your network adapter(s).
Continue your ping diagnostics, you said that you can ping the router, make sure you can ping both the inside edge and the outside edge (WAN ip Address), ping your ISP's DNS servers or ping google (64.233.169.99) and
www.google.com.
If the google ip works and the FQDN doesn't then perhaps there is an issue with DNS resolution.