If he has broadband, then probably he already has a crossover cable between his computer and his modem (whether it has a router built in or not -- a router doesn't need to have an integrated LAN switch), so he might have an address problem rather than a cable problem.
Since he asked "How do you find the IP of the AZbox?", it seems pretty certain that he has an "address problem".
Re crossover cable to modem, I don't know about DSL or cable modems, but my satellite internet modem is apparently one of those connections that auto-senses what kind of connection it's attached to, because I can use a straight through cable regardless of whether I'm going direct to a computer or through a router.
Re the O.P.'s " How do you find the IP of the AZbox?" question, if you go to the setup page, and then down to the INTERNET page, it will allow you to see what your IP# is. I have mine set as a Wired network with Static IP, however you can also set it up to take a Dynamic IP# if you wish, however if you have multiple devices on the lan, the IP# might change. I prefer to set it as static so that I know for sure what it is.
If you set it as static though, you have to set it in the same subnet that your computer is in, so then the question becomes what is the IP# of the computer on the lan. That can also be static or dynamic, and again I prefer static. If you don't have a router or some other computers on the lan, I'm guessing that the IP# may not have ever gotten set, because I think it defaults to dynamic, and if there isn't a DHCP server available, I think it just gives up after a while. I have my computers set as static in the 10.1.x.x range, mainily because it's easier to remember than those 169.254.x.x subnets. However to find out what IP# the computer is using , one way is to go to a command prompt window (start/programs/accessories/command prompt on XP), or start/run , and type in "IPCONFIG" without the quotes. This will tell you your IP# on the LAN, and also the IP# of your gateway to the internet, be it a router or whatever. IF you have multiple NICs , make sure you're looking at the right one, but you'll probably only have one, or perhaps two, like a wired and wireless.
If you want to change the IP#, or set it to static, you generally right click on "my network places" (if you're using XP or win2k, but I have no idea if you're using vista or 7). Once you right click you can go into properties, choose TCP/IP properties, and it will allow you to choose the default dynamic, or select a static IP# of your own. Use 255.255.255.0 for the mask, and you'll also have to enter a gateway and DNS server IP#, which is usually that of your router if you have one.
Whenever I have a problem figuring out what IP# are being used on my LAN, such as that of my router, etc, I use a nice little freeware or shareware program called IPSCAN.EXE. You have to tell it which subnets to scan, but once you do that, it gives you the address of everything that responds on the LAN, along with it's name if it has one. Pretty handy.