One key reason your laptop might not boot up without a battery is the power settings in the BIOS or UEFI. So, make sure that power-related settings are correctly configured in the BIOS/UEFI. First, ...

You may access the HP Recovery Manager at any time by restarting the computer and pressing F11 repeatedly before the Windows logo screen appears. In the System Recovery panel, click Next. PC Recovery ...

1] Is your laptop fully charged? This is the first thing that you should do. Check if your laptop is fully charged or not. If the battery of your laptop is drained out completely, it will not turn on.