MacBook does not turn on without plug in.

my Macbook air does not charge so I change it to new battery, the screen indicate the battery has 36%of power, but I still can not turn it on without plug in,

no matter how much power is remain in the battery, it turns right off , if I unplug it.

I think, the problem started with sound, This Macbook Air did not have sound for a while, and then sound came back after a while, then started this power issue, in the beginning of power issue, I charging is on and off sometime s it charges and led was on the megafacee, but it was getting worse and now no led on megaface at all and no power without plugging in. what is the solution for this???? and can I fix this problem with replacing I/O Board??

anybody give me an answer..