Rebuilding aMacBook 1.83 GHz Intel Core Duo, hard drive failure so rebuilding system. Aircard will not stop self-assigning IP address. Any ideas how to resolve successfully?

Question

Had hard drive failure on MacBook 1.83 GHz Intel Core Duo, so had to rebuild the OS on new drive. Was on Lion 10.7.5 prior to failure, but had to reinstall Snow Leopard 10.6.3 since that was most recent OS on media I had.  After finally getting ethernet connection to router working, was able to get to internet and download / upgrade to 10.6.8.  I assume I can probably buy the upgrade to Mountain Lion 10.8 from there.
Problem is this, Airport will not stop self-assigning IP address for my wireless connection, and unless I can get wireless back on this laptop, doesn't make a lot of sense to continue the rebuild and reinstall of all the software that was on it prior to HD failure.  Only way to my home network and router is ethernet now.  Everything else on my network (Apple MacBook Pro laptops, iPhones, desktops, and non-Apple printers and laptops) is hooking up to router wirelessly fine.
Any ideas how to resolve successfully so that the airport will stop self-assigning and allow the router to assign the IP address?

Answer 1

When see the beachball cursor, note the exact time: hour, minute, second.  
These instructions must be carried out as an administrator. If you have only one user account, you are the administrator.
Launch the Console application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
The title of the Console window should be All Messages. If it isn't, select
          SYSTEM LOG QUERIES ▹ All Messages
from the log list on the left. If you don't see that list, select
          View ▹ Show Log List
from the menu bar at the top of the screen.
Each message in the log begins with the date and time when it was entered. Scroll back to the time you noted above.
Select the messages entered from then until the end of the episode, or until they start to repeat, whichever comes first.
Copy the messages to the Clipboard by pressing the key combination command-C. Paste into a reply to this message by pressing command-V.
The log contains a vast amount of information, almost all of it useless for solving any particular problem. When posting a log extract, be selective. A few dozen lines are almost always more than enough.
Please don't indiscriminately dump thousands of lines from the log into this discussion.
Please don't post screenshots of log messages—post the text.
Some private information, such as your name, may appear in the log. Anonymize before posting.