Battery vs Logic Board?

Hello a couple of days I noticed that my computer was about to turn off because I had 3% battery life left.

As I procceded to get the charger, I plug it in, and the computer shut off. I noticed the magsafe did not change color, so i tried a another charger, no dice.

Then when i connected my charger, then I did a SMC reset, and I noticed that the light did not change color. I pressed the power buttton, and heard the apple chime, within a couple of seconds the computer was off again.

Being that this was a mac without a removable battery, I very carefullly anaylized the situation, and removed the battery, I plugged in the computer via AC power and it booted, normal. I tried again with the battery, and again it shut it self off. I removed the battery, and contiuned to use the laptop as a desktop, until I was able to get it to the apple store.

A couple of days later, the AC adaptor provides me with the same symptoms as if I had the battery in. Boots up, and shuts right back down.

Now Im wondering if the AC adaptor can not give the compuer enough energy for boot up. but then that does explain why it was running on AC for 3 days.

So my question is, is it the logic board?

My Apple care is over, and im scared to know how much this repair is going to cost.

mid 2009 unibody Macbook pro

2.53 ghz

stock ram

SSD MOD