Do you have a crawlspace? If so, where is it in the house, is it dirt, or is it outside underneath, say, an addition?
If you're getting down on your hands and knees and don't smell that smell, then I'd think it's not coming from the carpeting or the padding or 'old' animal urine. What's underneath the 1st floor where you smell it most? And since you most smell it when the AC is off and when the house has been close up, are there rooms/places in the home under these conditions that you DON'T smell anything (like you smell it in the hallway but NOT in the bedroom(s))?
It is possible that you have had wet insulation and the wood is rotting but w/o tearing down a wall, it may be heard to tell. If there's access to an attic, go up there and look for signs of water damage. You would see things like water-rings, rotted or soft wood, and the like. Look especially near the walls where you smell the odor down below. Oh, and when did you first start smelling the odor? When you first moved in? After guests left? Etc., etc..