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.
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, ...
The best way to save battery on a Windows PC is to adjust your power mode settings, and reduce your brightness.