My wi-fi shows limited connectivity?

I have been using ZXDSL 513B Type II modem on my desktop with a cable.

Recently I bought a new laptop and tried connecting the wi-fi from it. But, although the network connects and shows full strength, i'm unable to use the internet on my laptop. It shows limited connectivity. Is there any way of overcoming the problem. The wi-fi does not work on my Lenovo A7000 (cell phone) either.

Added (1). My laptop is HP with windows 8.1

Do you have any devices that work with your Wi-Fi? If not, then the problem is probably settings in your router (ZXDSL 513B).

On your laptop, when it indicates it is connected to Wi-Fi, right click on the network icon at the bottom right of the screen and select Open Network and Sharing Center. In the window that opens, look for the Wi-Fi connection and click on it. This should open the wireless status window. In this window, click on the details button.

You should now have another window that shows various information about the Wi-Fi connection. Look for the IPv4 entries. The important ones are:

IPv4 Address
IPv4 Subnet Mask
IPv4 Default Gateway
IPv4 DNS Server

Apart from the mask, these should all start 192.168.1… The mask should be 255.255.255.0. If the IPv4 Address starts with 169.254… Then it means that the computer is not getting its address automatically from the router.

Repeat the same steps on your desktop and compare the IPv4 information you get back. Apart from the IPv4 Address, the other information should be identical. The IPv4 Address should be the same for the first three number groups, but different for the last one.

Please add an update to your question with the details you have found from the steps above. I will visit this question again in a few hours.