I'm another one to report same charging issues. It must be a design flaw somewhere.
For me, it started the first time I ran the phone dryout of battery power. Plugged it in the Samsung factory wall charger and experienced the "vibrating loop" others have reported, where the phone vibrates a short burst every 5 seconds in a continuous loop. Once I got a short screen display, but most of the time it shows a black screen (like it's dead) and the RED LED on the upper righ that normally comes on when the phone is turned off but charging DID NOT show up.
I had the phone replaced, where I resued the original battery, and the new one behaved exactly the same. So then they (Verizon) replaced the battery (all this unde a factory warranty coverage), and the new battery worked perfectly, for a few days. Then, as others have noticed, when the battery was run down to low or no power, the phone (with this new battery) started acting the same way.
Today I called Tech Support and got a guy who came across this and sai is has soemthing to do with the power capacity coming out of the charger. He told me to see if I plug it into a PC or Laptop USB port, if it will start charging..... I did, and it worked. He said that it appears to kick off when the charging source is a lower MA type, like 500 MA. But i ti's the 1A or 2A type, it goes into this state of "vibration loop" and the charger does not kick in. He said to charge it up to about 10% or more, then move it to the standard (higher power) wall charger, and it should kick in.
I let it charge on the PC to about 70% charge, and then moved it to the wall charger, but I did not see that same result - instead, with the phone left "on" the wall charger was not recognized. I then turned the phone "off" and plugged it in the wall charger, and again it when into the "Vibration Loop" symptom. Moving it back to the Laptop USB port started the charging right away. So, it coudl be the power amperage capacity is the issue, where a lower power (500ma) charger works fine, but a higher capacity (1a or higher) doesn't.... or it coudl be a PC ro Laptop is sending soem signal to the device over the USB port that jump starts it into charging. In any case, this is a problem that can be reproduced and Samsung should be able to come up with an explanation and fix.
:-$