Why is the charging port not recognizing the charger cable?

@karrinavaldez first you want to check your power supply. Make sure it has the proper voltage. Check to make sure that connectors are not bend etc. Check the DC-in jack of your laptop. Make sure there is no corrosion, debris etc. that prevents it from working. Clean it of any debris etc, use a few puffs of air to clean it out. If none of this works, get a ammeter and see if your laptop draws any amperage from the charger. After that, you need to check and see if your motherboard even gets power. For that of course, you need to open it up. Post Some good pictures of what you see. That way we can see what you see. Adding images to an existing question

To work on this use the guides Lenovo IdeaPad Flex 5-1470 from here. Or you can use the hardware maintenance and service guide for that. You will find that on the same page under the Documents heading