A very quick assessment based on what you are saying - and if you included all of the facts - would lead me to believe that the wall charger may be bad and the USB port on your Windows machine is not supplying enough power to charge the iPad.
Try another power adapter/wall charger - try another wall socket. It is really hard to say exactly what the problem is in this type of situation.
Could be the charger is bad so won't work on the wall...the HP laptop may not have a high power USB port, many laptops do not. The MBPs, except for much older, have high power USB ports so you can charge your iDevices.
Also, you might want to try a different cable to connect to your charger to make sure there isn't some problem there.
You can take it all to a genius bar and have them test the parts to find out if one or more are bad.
I guess it is possible that the dock connector port on the iPad is going bad but why it charges when connected to the MacBook is a mystery. As Ralph suggested - an appointment at the Apple Store would probably be your best bet to get an answer.
I don't think this will do any good but it is harmless and easy to try - have you reset the iPad?
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
You are not the only one confused by the charging issues. Yesterday I brought in to the apple store what I thought was a bad charger and left with a new iPad. When I got home I experienced the same problems that I had with original ipad2 and charger and that the apple tech experienced with my original ipad2 at the store. I have concluded that this is an unresolved design issue with both the iPad and the 10 watt wall charger. I got it work by using a different electrical outlet in my house. Originally, I was using a kitchen outlet that is on a circuit with a ground fault interrupter and other appliances. This is a 10 year old house with no shortage of power or at least no worse than my Apple store that's in a fairly new building. I then tried it in the family room that is on a circuit with just as many appliances but no ground fault interrupter and voila it works! Consider also how USB charging does not work from the USB port on my monitor, but works fine when plugged directly into the PC's USB port. Conclusion? Both of these devices work under ideal conditions, but just barely. Under real life conditions, sometimes yes, sometimes no. Apple I love thee, but please fix the problem. You're the only one that can.
The iPad is not like the iPhone. Thats why it has a 10 watt charger instead of 5 watt. On certain computers you will get the "Not Charging" Symbol while its plugged in because its not supplying sufficient power for the iPad to believe its charging, in some cases it might actually be charging it up.
The only test to try is get the original charger and plug it into the wall outlet. Does it charge? If it does then you have no problems.
In your case its probably the original power block, try another one.
The quickest way (and really the only way) to charge your iPad is with the included 10W USB Power Adapter. iPad will also charge, although more slowly, when attached to a computer with a high-power USB port (many recent Mac computers) or with an iPhone Power Adapter (5W). When attached to a computer via a standard USB port (most PCs or older Mac computers) iPad will charge very slowly (but iPad indicates not charging). Make sure your computer is on while charging iPad via 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.
Apple recommends that once a month you let the iPad fully discharge & then recharge to 100%.
At this link http://www.tomshardware.com/reviews/galaxy-tab-android-tablet,3014-11.html , tests show that the iPad 2 battery (25 watt-hours) will charge to 90% in 3 hours 1 minute. It will charge to 100% in 4 hours 2 minutes. The new iPad has a larger capacity battery (42 watt-hours), so using the 10W charger will obviously take longer. If you are using your iPad while charging, it will take even longer. It's best to turn your new iPad OFF and charge over night. Also look at The iPad's charging challenge explained http://www.macworld.com/article/1150356/ipadcharging.html
Also, if you have a 3rd generation iPad, look at
Apple: iPad Battery Nothing to Get Charged Up About
Apple Explains New iPad's Continued Charging Beyond 100% Battery Level
New iPad Takes Much Longer to Charge Than iPad 2
Prolong battery lifespan for iPad / iPad 2 / iPad 3: charging tips
No. There is a real issue charging the ipad2 with the charger provided given real world situations. Just after my previous comment, where I had my ipad happily charging on the circuit without GFI, I checked and it was back to Not Charging 88%. Left it alone with the smart cover closed, ten minutes later: Not Charging 88%. I plugged my wife's ipad into the same power block and cable - bingo it's charging! Plug mine back in - it's charging. Bring it back into the kitchen with the GFI - it's charging. Ten minutes later: Not Charging. Plug in my wife's: Not Charging. Perhaps the voltage in my house varies too much for the charger/ipad even though lights don't flicker and nothing else fails to work. If that's the case, then the voltage varies too much at the Apple store as well. Either that or all 3 iPads (my original ipad2, my repacement ipad and my wife's) are all broken. That's pretty far fetched. I've also seen Not Charging at my office, but never had the time to fuss with it.
All 3 of the iPads I've referred to are the new iPads (iPad 3).
Initially, I thought that the charger might not charge unless the iPad was below a certain point. But no, it happens in the 50-70% range as well. Yes, these are all wall chargers with no extension cords or such. It's sporadic. I haven't figured out if the air conditioning cycle has anything to do with it, but I think not. And the same thing happened at the genius bar. They plugged my charger into their ipad and it worked. The plugged their charger into my ipad and it read Not Charging and gave me a new iPad. Bring it home, same problem. I've got 3 10W chargers and cables and two iPad 3s. Same inconsistancy with all combinations of charger, cable, ipad and electrical outlet. All I can say now is that I believe the outlets on GFI (kitchen and bathroom) seem to yeild more problems than ordinary outlets. But with the ordinary outlets also a problem, I just can't be sure. If you read through the posts, you'll see that most of the charging problems are either using a computer's USB port or a 5W charger designed for iphones and ipods. However a fair number of complaints are similar to mine.
I will check my ipad while its pluged into the wall to see if I get this.
When its plugged into the wall do you actually get the "Not charging" in top right or does it just no longer show the icon that its charging?
And with 5w charger or USB port its normal to see "not charging" it doesn't supply enough power for the ipad to recognize its charging.