Sadly, your battery doesn't seem to be getting a full charge (or any charge at all). Having the battery disconnected only results in the same problem because nothing is really changing.
By this, I mean that there may be a faulty connection for your laptop's charger, it could have been broken in many ways but normally can be due to fatigue or just normal ware and tear.
Take the computer to a local repair shop and see if they have a way to charge the battery without it being connected to the computer, or if they have a replacement battery for you to at least try out to see if this really is the problem. A small store is probably better than a large chain like Best Buy in this case, simply because they have less protocols to follow.
I'm having an issue with my HP Compaq laptop. I had this same issue around six months ago and by some miracle, it corrected itself around a week later.
However, the issue has come up again.
I'll hit the "power" button and the lights will turn on for a few seconds. Sometimes it shuts down a second or two later, other times it'll stay lit up for roughly thirty sections and during this time I can hear the fan start up a bit. But then it all shuts down and I'm back to square one again.
I was told this issue could be caused if windows was making a critical update and the update was interrupted partway through. Not sure if this is just a theory or if other people have experienced the same.
I tried taking out the battery and just plugging the power cord in -- no luck.
Someone suggested taking out the battery and the power cord, holding the power button down for 45 seconds, then attaching the battery and plugging the power cord back in... no luck there either.
Does anyone have any ideas?