Does your charger sit all the way flush with the bottom of the iPad? It's possible there's just some crud in there that is preventing the cable from making good contact. Have a look into the port with a flashlight and if it looks like there's anything stuck, use a toothpick to try and fish it out. Just be as gentle as possible to avoid damaging the pins.
Agree to the previous answer regarding the need for solder know how to complete this repair. That being said, I wouldn't give up if you aren't personally comfortable with the repair. There are lots of repair shops that can do this repair. I would see if there are any mobile device repair places local to you that do this. Ask people you know if they have any recommendations.
As for an iFixit Guide. There are lots of good YouTube videos for this (I might have to do some sleuthing to find a link) Its actually not a terribly difficult solder job as far as iPad repairs go. But it does require some specific tools. And I wouldn't recommend it to someone with absolutely no solder experience. But soldering is fun. And it's less intimidating than people think. It just takes practice.