Hey--
I had a similar issue with an Inspiron 11 3147. It wouldn't charge, so I assumed the battery was completely useless and ordered another. After I replaced the battery, the charging issue remained.
Unlike Latitudes, the Inspiron has a smaller charging plug. The plug has a hollow center that mates with a recessed pin in body of the laptop. That pin was bent, so the charging plug wouldn't insert fully.
I used needle-nose pliers to straighten and center the pin, and carefully inserted the charging plug-- noting that it went deeper and "clicked" into position. With the plug inserted properly, the laptop charged fully and worked fine.
Good luck, HTH.