That is the conundrum DIY fixers face. If you haven't already done so, open up your iPad. The battery is usually the part that needs replacing. Still, once you have removed it you can probe it with a multimeter to see if it is holding a charge. At ~4.2V, it is pretty much full and at 3.5V it is pretty much empty.
If the battery is holding a decent charge and you're not getting the charging symbol, you may have a defective charge port or logic board issue. If the battery is dead, then it's probably the cause (but it could still be something else). If it looks like a charge port or logic board issue, it will require a micro-soldering repair and is not DIY.
Ultimately, the only way to know is to try known-good or new components.