iPad only charges up to 1% and at that, only if charged from 0% I plugged my iPad 3 in order to charge it. However, after a couple hours I noticed that it hadn't been charging. 

It goes like this: First, it's completely off. Then, I plug it and charges up until it is on again with 1% battery and it won't charge any further than that. If I shut it off or the battery drains again, the same thing happens again.

Just one more thing, twice instead of the Apple logo, there was the iTunes icon. The iPad stayed like that but went back to normal after a reboot.

I have never had any problems with it, any ideas?
It sounds like its about time to buy a new cable and possibly an ipad charger. I go through cables all the time on my iphone/ipad. They always get frayed where the cord meets the lightning plug. 
Go to best buy and buy a new one, worst comes to worst, you can always return it. If the new cable doesn't work, its time to call apple and send it in for service.