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 can fix your battery without buying a replacement.
It's worth exploring options to preserve battery life before replacing your battery outright. Generating a battery health report on your Windows laptop is one way to see if you may need a battery ...