Based on the information provided, it seems that you are experiencing a backlight issue on your MacBook after replacing the battery. Here are a few suggestions that you could try to troubleshoot the issue:
# Check the backlight fuse: The backlight fuse is responsible for supplying power to the backlight circuit. It's possible that the fuse may have been damaged during the battery replacement process. Try checking the fuse with a multimeter to ensure that it is still functioning properly.
# Check the backlight cable: It's possible that the backlight cable may have been damaged or not properly connected during the battery replacement. Try disconnecting and reconnecting the cable to ensure that it is properly seated.
# Check the voltage on the backlight pins: According to the schematic for the 820-3536-A logic board, pins 1, 8, and 28-30 on the display connector should have a voltage of around 12V. A voltage of 52V on pin 1 seems high and could indicate a problem with the backlight circuit. Try checking the voltage on the other pins to see if they are within the expected range.
# Contact Apple or a repair professional: If you are not comfortable performing the above steps, it may be best to contact Apple or a repair professional for further assistance. They may be able to provide additional troubleshooting steps or arrange for a repair if necessary.
I hope these suggestions help resolve the backlight issue on your MacBook. Good luck with your repair efforts!