Have you used a multi-meter to make sure the AC adapter is putting out the proper voltage and such? If it's not putting out the proper voltage, you'll need that replaced, or you can go get one of those multi-setting ones that may work. The proper voltage, amperage, and polarity for the plug will be on the AC adapter.
If the adapter is putting out the proper voltage, test the laptop with no batter installed. See how that works.
If the laptop isn't working properly with AC plugged in, no battery installed, then you have a bad DC - DC inverter board.
If the laptop works ok with AC plugged in, and no battery installed, you have a bad / shorted battery.
In either of the last 2 instances, you will have to speak to the manufacturer, and get it fixed hopefully under warranty if possible.
If it's not in warranty, then you really have to decide if the cost of repair is worth it to you, or if you'd be better off replacing the laptop. DC-DC inverter boards are NOT cheap items to replace. I've had to replace a number of them over the years for customers. It's never happened to me personally, but if it ever did on a laptop that was out of warranty, I'd be parting out that laptop on FleaBay or something.