Some definitions
ISP (Internet Service Provider) - This is the organization that connects your system to the Internet. Since you mention that the cable and the internet went out at the same time, I assume that your cable provider is also your ISP.
IP address - With IP version 4, this is a set of 4 numbers from 0 to 255. For example, when I connect to www.cnn.com, my system uses an IP address onnections to www.apple.com
Domain name address - This is a group of words connected by periods, such as www.apple.com or www.cnn.com.
DNS (domain name server) -- This is an online service that acts like a telephone book, giving you an IP address when you send ita domain name address. Interaction with the DNS is done automatically by other applications on your system, such as the internet browser (Safari, Firefox, Internet Explorer, etc.) The DNS will sometimes give you a different IP address depending on where you are. The IP address given in Mexico may be different than the one given in Canada or USA, because it will give a more local number.
If your Internet connection for your house uses DHCP (dynamic host configuration protocol), it will obtain the IP address for the cable rounter and the DNS system when it connects. This is called a DHCP lease, with the idea that your cable box has leased an IP address from the ISP which should be yours until it expires. (The expiration time for the lease is also given during the initial communication.) When you renew the lease, you are asking the DHCP server to keep the IP address longer and get a later expiration time. If the system can't renew the lease, it will give you a new IP address and a new expiration date.
The cable box acts as a DHCP server when talking to your MacBook, iPod, computer game, etc. This means that the DHCP gives you an IP address for each device together with an expiration date. (This address is from a special pool that can only be used within a local system.) It will also pass on the address of the DNS server.
Now suppose you enter http://157.166.241.11 into your internet browser. If CNN appears, it means that all of your DHCP leases are good. If it doesn't, you may have a DHCP problem. Rebooting the cable box will cause it to renegotiate the DHCP lease with the ISP. Rebooting each of the routers in turn followed by the end device will cause them to renegotiate their DHCP leases. I have found that this sometimes resolves problems like you describe.
If you get CNN when you enter http://157.166.241.11 but not when you enter http://www.cnn.com, it means that you may have a DNS problem. Your system can find a system using an IP address (think of it as a telephone number), but it can't find the IP address for a given domain name. (Think of it as not being able to find the telephone number in the telephone book, or possibly it can't even find the telephone book.)
People normally use the DNS supplied by the ISP. However, there are many other DNS servers out there. What the previous comments are saying are that two of these are at the addresses 8.8.8.8 and 8.8.4.4. Any number of people can use a DNS server. It identifies the location of the telephone book, not the location of your device. If you enter the addresses of those DNS servers in your configuration and you can then access http://www.cnn.com, you are having a problem with the DNS servers supplied by your ISP. They could be out of service or simply taking so long to respond that your system is ignoring them. Alternatively, the DHCP server could be giving you the wrong address for the DNS server.
When my daughter was at college, I changed the DNS address from the one for her apartment building to the one supplied by the college. The one used by her apartment building was apparently very overloaded.
If your area is using IP version 6, the IP addresses will be eight numbers separated by colons. The numbers will be hexadecimal, meaning that the digits go from 0 to 9, then from A to F.
Try working in this order.
Enter http://157.166.241.11 in the browser. If this doesn't work, try rebooting all of the devices in order from the cable connection to the individual devices.
Try connecting your computer directly using an internet cable to the box supplied by the cable company. If this works, you may have a problem with the routers in the middle.
If you can connect using an IP address but not using a domain name, try entering the addresses for the DNS servers in your network configuration.
If the DNS addresses work, you can use the same addresses for all of the other devices.
<Edited by Host>
