My HP Pavilion m6 laptop will turn on and function properly when the power cord is plugged in, but fails to turn on (or return from hibernate) when on battery power. Interestingly, if the power button is pressed when the computer is off and the power cord is unplugged, it will immediately turn on once the power cord is re-inserted.
This is likely related to the fact that when the power cord is in, the computer fails to recognize the battery. If the power cord is removed while the computer is running, it operates on battery power without problems.
I have tried holding down the power button to reset and have tried removing/reconfiguring power adapter settings in the device manager.
remove battery let sit for at least a min for capacitors to drain, put battery back in (less than 50% chance of fix, but sometimes works and its easy). Fixes (bad contacts between laptop and battery) and (messed up firmware in laptop that gets reloaded after cold power up but not when there is battery power).
Download/install latest BIOS for your laptop. This might fix. Also, some laptops interlock the BIOS update such that they do not run if a battery is not installed/charged. If bios refuses to load because of no battery POST that.
Something is not working right in the charging/battery area. (duh). It could be the charging circuity on the MB. It could be the logic in the battery (especially if this is a clone battery vs. hp battery) . It could be problems with the contacts where the battery attaches to the laptop (dirt, etc).
Clean the contacts. When that doesn't help buy or borrow a new battery. When that doesn't work you are probably looking at a MB swap to get it working (and you now have an expensive battery that has no value to you). There are unfortunately no other replaceable parts. Swapping a laptop MB usually doesn't make sense unless you can find a cheap on on ebay from a lappy with a broken screen. A new PC is cheap and PC makers charge too much for the MB and there are no OEM MBs you can install. Assume you are out of warranty.
If you do look into the MB swap check youtube for videos. Usually someone has done a tear down on your laptop that will show you how to disassemble.