Chosen Solution
Sounds like you have a charging logic failure. Lets work this out from stem to stern. First lets make sure the MagSafe is the correct one and also in good shape. Review this Apple T/N Apple Portables: Troubleshooting MagSafe adapters Also inspect the contact pins and the mating surfaces on your system if dirty use a cotton swab (Q–Tip) slightly dampened with 85% isopropyl alcohol to wipe them down. Now lets plug it in and tell me what the color of the MagSafe cords LED bright Green, Amber, of dim Green.
Hi are you using the correct power adapter and not an aftermarket one, for the 15inch if your not using a 85w adapter the computer will not boot on a dead battery and will appear dead. I had a similar issue and it was my replacement power adapter was a rebranded 65w not an 85w.