2002 Pontiac Grand Prix Can you figure this one out!

Electrical problem
2002 Pontiac Grand Prix V8 Automatic 79,000 miles

I might sound a little crazy but I can't seem to get an answer to what is going on with my car. There seems to be some crosswiring or something that is going haywire. The symptoms: When I go to turn on my heat/ air on, it causes my running lights to shut off. The heat/air only works inconsistently. Now it is more often never working than working but sometimes I manage to get lucky. When I turn the heat/air back to "off" then after about a minute the running lights will turn back on. I am able to actually turn the lights on when the running lights are off. I have checked all the fuses and they are all fine. I had my battery checked and it was bad. I replaced it and still same problem. What could be the problem? Where do I take it? And how do I avoid spending a fortune? Thank you so much!