Blinking white simply means the tablet is communicating with the internet, checking mail, updating news, weather, etc. Stop fretting about that. Its normal.
As long as the power button turns orange when you plug it in, its ok. It might blink white, but it should go back to orange.
Also sometimes it will not get fully to 100%, or it will go to 100% and then stop charging and drain back to 95% or some thing.
That too is normal. Your charge controller does not know how low the battery can go, and it needs to be calibrated.
Just run the tablet down to the 2% warning, then plug it in and charge till its full.