2009 MBP won't boot unless power adapter is connected

Hello,

I found a similar question in the forum from a couple years back but there were no solutions offered. I think this is an uncommon problem and am posting in case any here have encountered it before.

It's an early 2009 17" MBP (5.2) and the battery was replaced about 3 years ago to try addressing this problem. It's currently running El Capitan.

The computer will instantly power off just after the appearance of the Apple logo if booting without the power adapter connected. A couple times the progress bar made it half way. Apple menu -> Restart will sometimes successfully restart, about 1 out of 5 attempts. The success rate may be a little higher if I boot in safe mode but I wasn't keeping a count, it just seemed that way.

The computer often won't wake from sleep either. The sleep light is blinking, open the shell and tap a key to wake and the computer just dies. I can turn the computer on with the power cable attached, disconnect it and then run out the battery with out any troubles.

Coconut Battery reports the battery to have 17 cycles and 13100mAh capacity. I drained / charged the battery a few times over the past couple days using a webgl sample and 'yes > /dev/null &' to tax the CPU. The computer would run for about 3 hours before shutting off. Each time I did this I reset the SMC as per the Apple support docs (disconnect the battery, etc.). I would them fully recharge the battery (~5 hours??) before booting.

Any ideas what this could be? A flakey battery - but the problem started with the original battery and persisted with the new one; intermittent logic board problem or perhaps even a firmware issue that's affecting some power management setting?

I appreciate any suggestions people may have. Thanks!

j