Help! Out of ideas!

Hello, Recently my silverado has been giving me some electrical problems. Yesterday, my truck was running fine. It was hot (100 + degrees) and I stopped at the store on my way home from work. When I came out and tried to start it, it only clicked. I got a jump and it started up, so I had the battery tested and replaced it. I also put in a new "in the box" alternator that I had already from a buddy. Truck started up and all seemed OK. Today, when leaving work, same clicking deal. I disconnected the neg bat cable and reconnected it to ensure good contact. Started right up. This continued throughout the day. Also hot BTW. I also noticed that the fuel and temp gauges self check ok when ignition is turned on and work good when running, but when I shut off the truck and remove the key and close the door, as soon as the dome lights go out, the temp and fuel gauges float up, as if they are getting power. When I open the door, they go back to no reading or the rest position. Then, once again, close the door and dome goes out, I hear a click and up the gauges go. They also return to normal if I just simply put the key in the ignition or if I arm the keyless entry. But as soon as it arms and the lights go out, click! Gauges moving up. Fuel gauge shows at 3/4 full when this happens and temp varies. Hope I have given you enough info. Any help would be greatly appreciated. Thanks Oh yea, 2001 silverado, 4x4, Z71, x-cab, 60K, 5.3L, Auto w/push button 4x4.