When troubleshooting charging issues, I would do the following (in order):
Always try another Lightning cable and charger, preferably Apple
original or MFi certified units.(You've already tried this, go to
the next step)
cable 8-pin connector] should be sitting flush with the housing and
completely inserted. If it is not, there could be lint/dust/debris
inside the port impeding a proper connection. You can clean it out
with fine point tweezers or a dental pick. Just be careful not to
damage the pins inside the Lightning Port.
Change the battery. The battery is the weakest link in the entire
device and certainly for charger related issues. Unfortunately, it's
a not a trivial repair on an iPad. If you can get the device to boot,
the use a battery utility, such as coconutBattery (for Mac) or
3uTools (for Windows) to test the battery prior to removal. Anything
less than 70% of design capacity will require replacement.
If the battery is in good condition, you can use a USB Ammeter to determine if the phone is really drawing current when it says it's charging. If it isn't drawing current, then I would change the Lightning/Charge Port. This is also a non-trivial repair as it requires some micro-soldering.
If a new battery and charge port still don't resolve the issue, then you either have faulty replacement parts (possible) or a logic board issue.
If you are up to the challenge of opening your iPad, then there is an IC (commonly referred to as Tristar) responsible for communicating with the charging device and uncertified chargers can damage it. Unplug the battery and connect a known-good (preferably Apple original or MFi) charger to the device. A properly working device will show an Apple logo and boot loop. If the Tristar IC is bad then the device will not do anything.
Because you have critical data, you can't just bring this to the Apple store because they will only offer you a replacement device. If you need to save this data, then follow the steps outlined above or find an independent repair shop to do some tests. If the problem is at the logic board level, then a shop that does micro-soldering repairs may be able to save your device or your data.