how do i know if i need a new battery in my iPad 2

Try a different charger. If the battery does not hold a charge then you need to replace it. If you use the device on battery a lot, and it's two or more years old, then the battery is probably failing.

Most computers do not have enough power to charge an iPad. A iPhone can charge on a computer but not the iPad.

If the wall charger seems not to work try using a different wall charger. Remember that an iPad with a completely drained battery will not respond right away after plugging into a wall charger. Wait 30 minutes then reset the iPad. Press and hold both the Home button and the Sleep/Wake button continuously until the Apple logo appears. Then release the button and let the device restart. You will not lose data doing this. It's like a computer reboot. If the iPad restarts let the batter continue to charge until it is at 100%. If the iPad does not start up and you are sure the cable and charger are good, make an appointment at an Apple Store to have your device examined by a technician. Or contact Apple Support.

Make certain that you're using the charger that came with the iPad. Do not use an iPhone charger. Do not use an iPod charger.