There may be a lot of reasons for it, but chances are good your new battery is defective. The battery is not just a battery, but also includes electronics that communicate with the iPad and report things like current charge level and temperature. If that circuitry isn't working it can have all kinds of effects on the system such as the inability to charge the battery and possible software issues if its sensors can't be read.
If you bought the battery here on iFixit, contact them at email@example.com and they'll get you fixed up with a replacement; they have a 1 year warranty on batteries and are very good at honoring that warranty. If you bought it somewhere else, you'll need to contact your supplier about a return/exchange/refund. Despite the best efforts of any supplier, it's always possible for a bad battery to slip through whatever quality checks they do, so getting a bad one is far from unheard of.
The fact that it works fine with the old battery is positive proof that the new battery is defective.
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