yeah...tried that. They said to just go buy a new computer. Just bought this one a couple months ago. Not covered for a drop. I thought maybe it was the port where the charger gets plugged in that was damaged. Is there a way to charge the battery externally to see if it is the battery or the plug in thing?
It does sound like the charger socket might be damaged on the inside. These are often weak spots as they are subject to mechanical stress from the plug going in and out, especially if the plug doesn't "soft-lock" into place like a USB or Ethernet connector or screws in like a VGA, and of course if you drop it that won't do it any good.
I had a similar issue on a (non-Lenovo) laptop a couple of years ago. I hadn't dropped it but the original soldering was probably bad and I noticed that I had to plug the charger in at a certain angle and sometimes wiggle it around until finally it refused to charge altogether and then, once the battery ran completely flat, to boot at all.
I'd had the machine for a few years and it was out of warranty, but I took it to a third-party repair shop and they cracked it open and found that one of the plug's connectors to the mobo was broken so they soldered it back on, and the laptop ran fine for another couple of years.
The manufacturer won't cover this sort of repair and it will likely void your warranty, but if it's that or buy a new one it's worth it. Small repair shops can usually test the battery too to see if it charges at all, but I think it's more likely to be the plug if there's no visual damage to the battery or the battery-chassis connection.