I generally recommend starting with the basics; in particular, is your device getting power? That starts with your charger; you'll definitely want to verify that it's working, either by trying a different charger/cable combination or seeing if they charge a different device.
From there we want to see if your iPad is taking in any power; the easiest way to do that is with a USB power meter; you can pick them up for like $5 on eBay. If there's no power going into the tablet then I'd want to look at the charging port next; get yourself a magnifying glass and a bright light and check the port for dirt, lint or bent/broken pins. Clean the port with 90% or higher concentration isopropyl (rubbing) alcohol in conjunction with, say a toothpick and an eyeglass cleaning cloth.
That's going to be about the extent of what you can do without opening it up. Unfortunately the charging port on your iPad is on a cable that's soldered to the logic board, so replacing it requires a fairly high degree of soldering expertise so it's not like you can just throw in a new charging port hoping it'll help.
Alisha, ( @flannelist ), do you have any suggestions beyond what I've mentioned?
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