"not charging" means that your iPad is not receiving enough power to charge itself, but it IS receiving enough power that it is running solely off the power it is receiving through the USB cord. I would recommend trying to plug it into a different USB port on your computer, and perhaps to try a different cord if you have a spare.
Most usb ports do not provide enough power to charge your ipad, plug into a wall outlet to charge. If you leave it plugged into the computer and the computer goes to sleep, it can actually drain the battery.
IOS: Syncing with iTunes
Apple - Support - iPad - Syncing
Not able to sync with iTunes is a common issue. ANy or any combo of the below may help
Restart your computer.
Reset your iPad by holding down the sleep and home keys, past when you see the red power down slider and until you see the silver apple. Let it reboot and try again.
Try a different USB port
If you're using any hubs or extenders, stop and plug it directly into your computer.
Try a different cable.
Make sure your iTunes is up to date and is the latest version
Go into the control panel and 'add/remove programs', look for Apple mobile device (something) and uninstall it. It's just the driver that tells your computer what to do with the iDevices. Uninstalling it is harmless in that when you plug your device back in it'll reinstall.
Uninstall and reinstall iTUnes.
If your mobile device driver gets lost or corrupted you have to try several tricks to get it to reactive/reinstall. That's what the above will do. Any one or any combo may work. Unfortunately, there's no single 'silve bullet fix'
ipad 3 requires large amount of power. Many PCs doesn't provide enought for it to run and charge at the same time.
- try differet USB port in computer (that could be providing more power)
- try different computer (most Macs do provide enough to charge iPad)
- use iPad charger to charge
- you can turn iPad off. That way in doesn't require power to run, and should charge (albait, slowly) on most USB ports.