Try a power refresh just in case it is a corrupted BIOS.
There's no RTC (Real Time Clock) battery on the motherboard in your laptop to maintain the BIOS settings when the laptop is turned off. The RTC battery power comes from the main battery.
Disconnect the charger if connected, open the laptop and disconnect the main battery and then press and hold the laptop's Power button for a full 30 seconds.
Reconnect the battery and re-assemble the laptop and check if it turns on OK.
Worth a try and if no good you've only wasted a bit more time trying to find the problem.
Here's a teardown video that may help.
If it turns on OK it may be prudent to create a battery report to check the status of the battery. In the report compare the Design Capacity value versus the Full Charge capacity value and then work out how good the battery still is i.e. Full Charge value as a percentage of the Design Capacity value.
Re your 2nd question, to my knowledge no HDD/SSD is required to be installed so that BIOS can be accessed.
The user manual for the PC will usually tell you how to access BIOS. Without a drive installed the PC will stop anyway as there's no OS found after POST.
If there was a Windows OS installed on a drive you mightn't get a chance to get into BIOS on startup due to fast startup being enabled in the OS and this minimizes the time to press the appropriate key to enter BIOS on startup. It's quicker than you are ;-)