samsung galaxy tab 3 not charging the 10.1 inch galaxy tab3 wifi version, is unable to charge
when u plug the charger in, the battery logo shows a bit, but it does not show the charging animation, neither it is charging

where the problem might be located

my skill is decent regarding soldering and so on, and I am willing to repair it myself

P.S. the tab does not boot due to dry and un rechargeable battery
My suggestion before you take the step of using your soldering skills, try using another charger, leave your tab connected with it for 3-4 hours, as sometime its just the charger that takes the toll of current fluctuation if that doesn't work, than Verify that your device port is not damaged. Carefully inspect your device's charging port and remove any debris. If all's well so far than verify that your Samsung Tab is running the most recent software. Just tap the System Updates dashboard -> tap Device Software. If an update is available, follow the prompts to install. Lastly is problem still persist it's time to perform a soft reset. A soft reset restarts your device and does not erase any of your content or data.Just press and hold both the Power and Volume up keys until the device turns off.

I hope this help, let me know the results.