Well first thing first. iTunes does not allow you to put incorrect firmware on a phone by default.
Which golden prong are you talking about? If it's the one connected on the side of the logic board. It gets contact to the housing of the iPhone 3 for reception / antenna I think.
The iPhone 3G battery has golden prongs which have contact to the logic board gold connection points which are located under the logic board and are aligned by default to have contact on the battery connector from the battery itself. There are screws specifically for this part on the logic board so the connection is good and firm.
Okay lets do simple troubleshooting steps to see if the battery may be at fault:
1. Connect iPhone 3GS to a iPhone usb cable (30-pin adapter) to a wall charger adapter. You should see the Apple logo go on and off. When it goes on again with the Apple logo appearing, unplug the cable straight away and if your battery is faulty, the Apple Logo should disappear immediately after unplugging the cable.
If this is the case, you will either need to reseat the battery or replace the battery. Has the battery expanded at all or do you notice the front display housing pushing up perhaps?