When you say you have "WiFi connection" at home? Are you talking about a "wireless home network"? What kind of router do you have?
HERE IS WHAT YOU NEED TO DO:
(1) "Hardware reset" your router: Use a pencil to push and hold the little button at the back of your router for 30sec and then let go. Give it a minute to startup. This will restore all the settings back to its factory settings.
(2) Therefore, you need to configure your router again, including the security. I recommend using "WPA2 Personal" and "AES". Use uppercase and lowercase letters, numbers and special characters in your password. Make sure its about 10 characters or more in length. Watch video links below on how to do this.
(3) Make sure "Maximum Number of Users:" under DHCP Server settings is set to the number of devices you have at home that connects to your home network. If that options exists on your router.
(4) Once that is done, add your network information (SSID, security mode and password) on your phone, and you should be able to connect it. Do the same for your computer.
How to setup D-Link router: http://www.youtube.com/watch?v=5KfSS1mi-YMv
How to setup Linksys router: http://www.youtube.com/watch?v=qHi4-kA9Jk4&feature=related
How to setup Netgear router: http://www.youtube.com/watch?v=ZbX-DHYJ4fk
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If you have a wireless home network, then you must have a "wireless router". You need to look into that and follow the instructions I have given you above.
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Your modem should be connected to your router. If you only see one unit there, it's possible that you have a modem/router unit, where both the modem and router are in one unit. This is given by some "Internet Service Providers" (ISPs). What is the name and modem number on it?