I just replace my laptop with new motherboard 2 weeks ago.,and it seem the problem is happening again.
When i turn on the laptop (with only plugged with AC adapter), nothings happen even there's no indicator lights on. But when i attach the battery (without attach to AC adapter), the laptop is turn on normally. Then i tried plug the power adapter back to the laptop, it seem that it doesn't charge the battery. Most weirdly, i pull out the battery (still plugged to the AC adapter), the laptop is running fine.
Allow you battery to fully charge for 24hrs even though it states its not charging also do a hard reset before you do so but don't power it up leave it as if it is charging after that if you still get the same problem your battery is probably bad, Some laptops will not start up without a battery attached once attached they run..
usually i can turn on the laptop normally without attaching the battery. I've done your solving method unfortunately nothings happened. Now i'm using the battery as a starter for my laptop to boot and then reattached the battery to save the battery power for future usage.