DR Jrand - As for your new Mac and the internet... Are you using dial-up or ethernet (DSL or cable)? If you're using dial-up, you "simply" have to "officially"recognize the modem via the Internet Connect settings.
However, if you're using an ethernet connection... If you've just been plugging the ethernet cable from one computer to another, then you will have an issue since most service providers only allow you to connect to one computer (via a unique IP address) at a time - unless you have a router to split the signal. However, there is a work around for this...
Just plug the ethernet cable into the new computer. Then turn off the computer. Then unplug the ethernet cable from the wall for a few seconds, the reconnect it. Then turn off your cable modem for a few seconds - the easiest way to do this is just to disconnect the A/C adapter cord - then turn it back on. Then turn on the computer. This should essentially reset your connection, and your ethernet connection should automatically be recognized by your new computer. Just open Safari to check to see if it is connected.
If this doesn't work, just give Apple a call. Some very helpful folks at AppleCare.