I have a Dell 9200 laptop. Yes it is rather old, but has served me well. It had been in storage about a year. It works fine if the PSU is connected. It shows the battery is fully charged. The battery test lights show the battery is fully charged. But, the computer will not boot up or stay on with just the battery.
Sometimes it will start to boot, then just turn off. If I boot up with the PSU and disconnect it, the computer will stay on for about minute, click and turn off. Then it will not even attempt to start if press the power button. If I plug in the PSU, all is well.