I've got an Acer Aspire 7750G that has been been completely disassembled dozens of times for various problems (worst computer I've ever owned, tbh).
It just started a new issue where pressing the power button to turn it on only works if the computer is plugged in. The battery is fully charged, and as soon as the light turns on, I can unplug it and it continues to load BIOS, etc... just fine. The power button works fine for turning off (actually set to hibernate) the computer whether or not it's plugged in.
It sounds to me like something internal where the computer is not recognizing that it needs to be drawing power from the battery. I had an old laptop like that years ago when I worked with slot machines. Fortunately for me, there was always a power source nearby.