Airport and ethernet show connection but I cannot connect to network

I have an iMac where I can connect to the internet within 10-15 seconds of turning on airport or plugging in cat-5 wire to use the ethernet connection. After this time frame I must turn airport off and then on to regain the connection. Or, if hard wired, I must remove the cat-5 and plug it back in. I have seen many posts similar to this on forums. However, all of the posts pertain to a wireless connection only. I have tried most all of the solutions people have offered including zapping my PRAM. Unfortunately, I have had no luck with any of them.
Three things to note:
1. I believe this problem occurred after a power loss at my home. No power surge - just lost power. I can't be certain on the timing but thought this should be mentioned.
2. I have upgraded from 10.5 to 10.6 to try to rectify the issue - didn't work.
3. I have switched from comcast to AT&T - different router/different connection/different network preference - and nothing changed.
So, the problem is not with the connection itself as I am able to connect for a few seconds. It doesn't pertain to the OS as I have upgraded and still no fix.

Thanks in advance for your help.

 

Thanks for the response Brian33. You are correct that I was referring to the airport card in the imac. The imac is a Core Duo. So, it is a bit old. After filtering with the word "network" there are many submissions that state "network configuration changed." What exactly am I looking for in the console?