New Macbook Pro turned off with full battery and will not power back on. 2nd time this has happened

I recently purchased a new macbook pro in mid January 2014, (3 month old computer)... About a month ago, I was using my computer and sat it down beside me on the couch (still open) when it suddenly shut down completely. I had about 80% charge at the time so it wasn't a dead battery. I tried everything to power it back on, including reset methods, plugged in, not plugged in, etc. etc. I called Apple support, did some troubleshooting, no luck- had to set an appointment. Went to Apple store and they took it to the back of the store and returned with my MBP working fine. The guy checked the hard drive as I sat there and watched, and everything checked out ok. He informed me that my battery was somehow holding too much charge and this was causing it to basically just shut down completely. It didn't make much sense to me but he advised me not to leave it on the charger too much and see how it went. I followed his advice. Everything has been fine until last night when the same thing happened again. I had the MBP in my lap, watching tv and it suddenly shut down. It wasn't plugged in at the time and I had over 40% charge. It will not power on now, tried everything, called apple support, etc. I have an appointment Friday but wanted to check here too. When I plug in the charger, the green light shows up faintly, but the computer will not respond at all. When I press the small round button on the side of the MBP where are all of the ports are located (battery indicator button) there is no response at all from the indicator lights beside of it. Not a single flash. Anyone have any suggestions?