First of all you need a case back press, such as this as it will be a very tight fit
https://www.amazon.co.uk/Watch-Repai..._source=1&th=1
As for the for battery issue, well I cant really offer much guidance. The battery and connection to the movement obviously works as the digital functions are working. Maybe there is a procedure to follow once the battery is fitted such as shorting it, or a button press combination.
Whats the Calibre of the watch?
OK seems to be a breitling Cal 75 and just a normal battery swap and resetting of the time and date functions.