I'd try it anyway, just to see what happens.
You should also restart and/or reset the iPad, if you have not done so since the problems started.
If it still does not seem to be working correctly contact Apple. If the iPad is less than a year old, or you bought AppleCare the battery should still be under warrantee for anything more than normal loss of capacity. If it's the battery, which seems most likely.
If not under warrantee, I believe Apple will replace the battery for about $100. Some third party repair shops will do it for less, but check to make sure they are certified and/or have a reliable reputation. If the battery is damaged when installed it can become a fire hazard.
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Restart: Hold down the power button until the power off slider appears. Slide it off. When the iPad finishes shutting down, hold down the power button again until the Apple logo appears. Apple recommends you restart the iPad at least once a month.
and then a reset if that does not work.
Reset: Hold down the power and home buttons until the Apple logo appears. The iPad will reboot. This usually takes a bit longer than a restart. takes a bit longer than a restart.