The battery chamber contacts & wires often corrode up. Did you see any corrosion within the battery chamber? The pins are clean and are not discolored? Getting to the chamber wires requires a fair amount of disassembly.
Review this service manual to locate the MG3 on the bottom of the camera so you can measure the battery power [http://jameskbeard.com/Photography/Legacy_Canon_Manuals/CANON%20A%20-%20SERIES%20CAMERAS/AE-1%20Camera%20Service%20&%20Repair%20Guide.pdf|Canon-AE-1 Service Manual].