It's usually the motherboard. Or a non-Toshiba battery. I'd call this in fast to see if they concur and how much.
My only other thought is how you got it to run on battery if it won't boot. I hope no one slapped in the battery while the laptop was booted. That could damage a motherboard.
My toshiba p505 wont boot with battery. will run on bayttery once running and has over 2 and half hours battery life. what could be the problem and how to fix it. thank you