Hi, Having a DS1307 with square wave output, you can be pretty sure if pin 7 will flash an LED at 1Hz it’s working,
then only a battery backup to retain the time that was set, and to not cause any shorts.

It’s been a while since I used a DS1307, but I’d start by assuming the chips are ok. Is the other board running same or similar code?
One way to go about finding the problem might be to make a throw away copy of the program that for every signal from pin 7 of the DS1307,
displays the time, increments the time, writes it to the chip, reads it back, and displays it again.