Here is a quick go with the info supplied.
The Ip address is what identifies your computer on a network.
Your adsl router or cable box whatever, will have an address assigned to it by your isp, this is the address that the outside world sees, with most systems it is automaticaly assigned and changes every time the box connects to the ISP's system, for your purposes that is of no real interest.
The box itself has an address that is used to id it to the computer this is local only address and only your computer will see it, almost every box will have the same or similar that it 192.168.0.1 or 192.168.0.0 or 192.168.1.0. normaly the first if you type that in the address bar of a web browser you will get a log in page and that will allow you to log into the box and alter settings. to log in you will be asked for user name and password, this will be in your paperwork somewhere, with a sky box its user name admin and password sky.
When you log in make sure that you have DHCP switched on.
Then have a look at your network settings on your computer and make sure you have DHCP switched OFF, you can only have one active otherwise both are trying to assign ip addresses and it wont work.
The way it works is that your ADSL/Modem talks to the ISP and has an assigned IP address the outside world looks at, it then assigns an IP address to each computer that is connected to it either by wire or wireless, most problems happen when both the box and computer are trying to do the same job.
Try going to START - all programs - accessories - command prompt, and then type ping 168.192.0.1 (assuming that is the address of the box) then press the enter/return key you should then see some lines of text saying how long it to to send a packet to the address and get it back, if you do that will tell you that the computer is talking to the box, if not then you still have a problem, if it is then your problem lies between the box and the outside world and that is the ISP's problem. But I suspect that your problem is that you have both your box and your computer trying to do DHCP at the same time.