Looking at the details for that your circa 2012 N1402 uses the X300 Ultrabook chassis which is now EoL. I wouldn't recommend upgrading to Windows 10 as that's not supported on that model.
However it does seem peculiar that you are now unable to access the BIOS. Windows 10 uses something called SecureBoot which would prevent access to the BIOS once installed on a UEFI compatible secure boot enabled unit, however this X300 is not UEFI compatible to my knowledge so it shouldn't have this effect.
Can you confirm that the issue persists even after physically disconnecting the hard drive/SSD from the unit?
Furthermore, have you attempted to reset the CMOS? This would involve disconnecting the watch battery from the unit.