The first "Batman" serial came out around 1942 and was an extremely low-budget affair. How low-budget, you ask? The Batmobile was nothing more than a gray sedan! In this very el cheapo serial, Batman and Robin attempted to thwart the plans of a Japanese scientist (played by J. Carroll Naish). I forget at the moment who played Batman and Robin.
The second "Batman" serial, entitled "Batman and Robin", came out in 1948 and featured Robert Duncan and John Lowery in the title roles. This one was more professionally produced, as it was handled by Sam Katzman. (Joel Schumacher and that shlockmeister of scribe, Akiva Goldsman, should have screened this serial to see how to get their "Batman and Robin" right!)
Bob Kane, Batman's creator, served as a consultant on both serials. He talked about the development of the serials in his entertaining autobiography, "Batman and Me".
I don't know if Sony had the video rights to the serials or not, all I know is what came out from GoodTimes Home Video. This leads me to believe that the serials are very likely in the public domain.