As it says on the page that you posted from :
iPad is designed to charge with the USB Power Adapter provided in the box. iPad will charge with any Apple USB Power Adapter and will also charge, although more slowly, when attached to a computer with a high-power USB port. When attached to a computer through a standard USB port (most PCs or earlier Mac computers) iPad will charge, but only when it's in sleep mode. Make sure your computer is on while charging iPad through USB. If iPad is connected to a computer that’s turned off or is in sleep or standby mode, the iPad battery will continue to drain.
If it shows not charging then it's probably because your computer doesn't provide enough power to its USB ports as described on that page - you will need to use the wall charger to charge it
If the iPad doesn't show on your computer's iTunes then is it a recent version of iTunes ? There is also some troubleshooting on this page : http://support.apple.com/kb/TS1538
I have tried most of what have been said here ( thank you for the great Job) but unforunatally it didn't solve the issue.
However, now the "Not Charging" message in the right corner disappeared and my iPad is charging normally from my laptop.
The reason behind that is using the USB3.0 port in my Dell inspiron N5110. Earlier, I was using the USB 2.0 ports and that is why it was showing that message but as sooon as I pluged it in the eSATA USB 3.0 port , the message disapeared and the iPad started charging normally.
So don't waste ur time here and there try to plug it to USB 3.0 port and it will works, Insha ALLAH.