IPAD WONT CHARGE FROM COMPUTERS

That because the USB on those computer doesn't supply enough power to charge the iPad. Your not alone... There a good majority of iPad user who don't have a computer that will charge the iPad. Use the wall charger.

If I connect my iPad to any PC, it still charges while the screen is off. The charging however, is very slow.

Read the article on iPad charging at the top of thIs forum, highlighted in yellow.

My iPad indicates that it is not charging when I plug it into my MBP, but if I leave it there long enough, it reverts to fully charged. Maybe your iPad is charging but not indicating that it is?

The LCD is the biggest drain on the battery.
If your USB port is not a high power port-it will not charge while the screen is active.

If you turn off the screen, the iPad will charge at a very low rate-usually.

To test, plug in the ipad, turn off the screen and leave it.
Check on it in an hour-did the battery charge go up a percentage point or 2?