MacBook wont turn on, magsafe remains green.

Hi , i have a macbook prob13" late 2011 model. The other night i shut down the laptop wid low battery ( around 4-5%) i didnt charge that night.. Next day when i tred to start up with the magsafe charger it didn't. When i connect the charger , it lights green and in the batter indicator 3 green light and fourth one blinking. The magsafe never turned amber. I tried SMC, resetting RAM, disconnected the battery and reconnecting , took out RAM and re installed it.. Nothing seems to work. I have taken to a service center but the technicians were not very helpfully. They told me its the logic boad and you have to change it. He didnt check much. He did it in fronth of me. He opened tried with the battery connection then he tried with a power cord. That was it what he tried then told me its the mother board. I wasn't satisfied with what he did.. So can anyone help me..Is this problem with the logic board or the magsafe board.. Thank you