iPad Air charging problems are very common.
A lot of times it is due to a bad charging port, specially since you explained how it was previously abused.
It is not a difficult micro soldering repair. Delicate, but not too difficult.
If you don't have soldering experience, I advise against taking it on as a DIY job. In which case you're better send it out or taking it for repair.
After the charge port has been replaced, you can test to see if the iPad is working correctly.
If still not charging properly (sometimes it charges only when the screen is ON), then you have one of those difficult cases and you need a seasoned technician to solve it. They can be a real PIA and I've seen very good techs pulling their hair because of them.
P.S.: beware who you send it to. A lot of wannabe techs pull the pads on the boards when trying to replace the port. For someone with the right skill, it is pretty straightforward.