A battery was a type of power source.
A 1936 Ford truck's engine was powered by a battery. In 2371, after recovering the truck in deep space, the USS Voyager's navigator Thomas Paris activated the truck's engine with a key. (VOY: "The 37's")
In 1937, Amelia Earhart's plane, a Lockheed L-10 Electra, was powered by a battery. Over four hundred years later, a distress signal from this plane was picked up by an away team from the USS Voyager on the surface of a Delta Quadrant planet. The team leader, Captain Kathryn Janeway, was skeptical that the plane's battery would be functioning after these many centuries. An investigation of the plane revealed that the plane's AM transmitter was being powered by an alien fusion generator. (VOY: "The 37's")
Three decades later, in the 1960s, batteries powered the descent stage of the Apollo Lunar Module. The schematic of an Apollo Lunar Module depicting the location of these batteries in the spacecraft was stored in the USS Enterprise's library computer database. This database was accessed by the Talosians in 2254. (TOS: "The Cage", remastered)
In later spacecraft, batteries were "demoted" from a primary power source to a tertiary power source. Also known as emergency power cells, batteries were used as an emergency backup to control gravitation and oxygen levels on starships. (TOS: "The Cage", "Where No Man Has Gone Before")
After the Galileo made an emergency landing on Taurus II in 2267, Spock and Montgomery Scott used battery power to electrify the exterior of the hull, in order to drive away the attacking natives. (TOS: "The Galileo Seven")
Later that year, the Enterprise was pulled into an alternate universe. Captain James Kirk called for emergency battery power to restore the ship's failing life support. (TAS: "The Magicks of Megas-Tu")
In the 2150s, emergency lights in the United Earth Embassy on Vulcan were powered by batteries. After the embassy was bombed in 2154, Travis Mayweather and Malcolm Reed detected a power signature which they believed was coming from the batteries. They discovered the signature was being emitted from an armed bomb that had failed to explode. (ENT: "The Forge")