If you have a LAN network as you describe it. The external IP address (might be 215.95.188.70) is assigned to the input side of your modem.
The modem gives itself an internal IP address. The are some choices for local area networks, but almost always the modem defaults the internal network as the 192.168.x.x network. The modem reserves default number 192.168.0.1 for itself.
If you want to connect a computer to the network, you can let the computer assign a local address for you. Then the computer takes number 192.168.0.2 or (192.168.0.3 if the other computer is connected).
When you fill in the properties of your internet-connection you must under tab properties for IP4 click on the radio button "automatically assign a IP address", then you cant fill in an ip address.
If you don't, you must fill in the IP for the standard gateway (192.168.0.1) the subnet masker 255.255.255.0 and the IP address 192.168.0.x where x is a number between 2 and 254.
If you choose to assign your own fixed numbers like that, you must remember to give every computer (better: every network adapter) its own number. And you better use fixed numbering for all your computers.
When you want to connect your laptop with a cable to your network you use a different adapter, so for that adapter you must also then choose a different IP number.
What did you do wrong:
1. You cant choose randomly you own IP address. You have got an IP address from you service provider, but that address is for the modem. The LAN uses internal addresses (as stated above the 192.168.x.x numbering) So your IP addresses must start with 192.168
2. Use automatic addressing on all computers or fixed IP addresses on all computers. If you choose the last select different numbers: eg. 192.168.0.2 and 192.168.0.3
If you want to see what parameter are used in the modem. Select http:/192.168.0.1/ in your browser. If you haven't changed the default, you should see a response from the modem. A series of pages, like webpages, where you can put in all kinds of parameters. Check the manual of the modem for its meaning.