First post and here comes the trouble .

I'm using a ADSL Modem from the ZTE Corporation model name is ZXDSL 831AII which works perfectly fine on its own, has 2 "out sockets" one being the standard LAN cable CAT 5, and one being a USB.

The trouble is I have 3 computers, so I bought a router (TP-Link model No. TL-R402M) which doesn't work. Well the router itself is fine, but when I plug in the LAN cable from the modem to the router and then from the router to the computers I get no internet connection. And I really have no clue what to do, I've tried configuring the router change the routers IP etc... And still nothing. Anyone got an idea on how to get it working please do share.

Thanks

Ethernet is not ADSL. You can't connect your modem to a router, esp. through the OUT ports. You need an Ethernet card for your router. What you describe you just can't do.

Isn't that just great... Would it work if I got meself a Hub instead?

You can use a basic netgear or any other router from best buy or another computer store. The thing is, you need to connect the ethernet from the dsl modem to the WAN port of the router. Then connect the switch part of the router to the 3 computers you have.
The modem gives you an ip address from the internet provider, the router then takes that one ip address and allows you to set up your own home private ip addresses, but they all use the internet ip address.

as regards IP addresses for the machines, try the reserve IP address interface and manually enter the IP address for your 3 machines with their mac addresses ( find the mac address by ipconfig/all in command prompt and the one under ethernet card is the one you should be looking at )

then try the static Ip interface in your router interface and do the same - at times the routers no other way of obtaining this info ( though since you aren't using wireless router I suppose it might not apply ) but just a secondary measure