I wouldn’t try replacing the connector if you are not experienced, as this is a double layer board which users low melt solder to connect the two layers. If putting pressure on the connector solves the problem it means the pins on the battery connector have most likely been pushed into the plastic and or the connector has been pushed out of shape. With some magnification and a pair of surgical tweezers you should be able to pry the pins out a bit and squeeze the sides of the connector a little bit so as the pins are all making contact and the connector fits back in snuggly.