I have a laptop problem?

Thus nothing works without the adapter.

The black-screen beep and shut down could be several things. A common issue is that the power supply connector is broken, such that the power supply cannot always supply adequate power.

While it sounds likely that your battery has failed, if the power supply brick is faulty or the connector on the laptop is damaged, then the battery will not charge.

The screen going black power-down sounds a lot like what a laptop does when it has a dead battery or a failing/faulty power supply.

It is either:
1) Battery needs charging fully.
2) You need a new battery because it is dead.
That is all i can say from your post, unless you give us more details on what you have done.
Now, do you give the laptop battery a chance to fully charge up?
If not then you will need to give it at least 8 hours to charge.
If you want to use the laptop when/while it is charging then give it half an hour and it will be fine, but leave it plugged in when you switch it off or power down.

Also read robo_dev's post as above.

all the hp 6xxx laptops have the same problem.
cuz the video chip and cpu are setting too close together.
You would need to buy a new laptop or to find someone who can reflow the chipset for you.
You can find that information on youtube as well.
But those guys do the chipset reflow without using a reflow station..... interesting.