Running into an odd boot issue, won't start without AC Adapter

Hi everyone,

CPU: Intel Core i5 2410M Sandy Bridge

GPU: Intel HD Graphics 3000

RAM: 8GB Dual Channel DDR3

Motherboard: Lenovo Base Board (40CN30WW)

I completed a vanilla installation of El Capitan on a Lenovo G570, am able to boot into the OS without the USB installer and got most of the important things working and was able to even run updates. Battery is working, shows the percentage and is able to charge. Once booted into the OS I can disconnect the AC Adapter and continue with the battery with no issue.

What part I got an issue with: The problem is that if the computer is shut down and the AC Adapter is not connected, the computer won't even start up. The light for the power button will turn on for a few seconds and then turn off. It won't even start up enough to get to the bios. But once I connect the AC Adapter again (though it takes a few tries pressing the power button) I am able to get back into the OS with no issue.

I have investigated this for some time, I have a secondary battery and ran into the same issue. Both batteries are original to the laptop. I've tried installing Windows 10 and Linux Mint, and did not encounter this same issue with either. I have even done a fresh install of El Capitan with the bare minimum, but cannot figure out what is causing this. I've searched online but don't see any posts relating to this issue. Any guidance would be much appreciated.

Thank you,