Fuel gage neddle drops to zero with the fuel tank is full.

Possibly a bad fuel level sensor. Check resistance of fuel level sending unit. If thats ok you may have a wiring issue in fuel level sending unit circuit.

For test procedures there is a company that independent auto repair shops get their information from, this same information is available inexpensively for people that work on their own cars.. The information is year make and model specific, covering repair procedures, torque specifications, fluid capacities and specifications, service bulletins, component locations, wiring diagrams ect.... Alldata is very easy to navigate http://bit.ly/AllData_Repair_Manuals_Online I don't think it would have anything to do with changing the battery or the other instruments would most likely be reading incorrectly as well.