The ‘Black Screen with Caret’ issue

There’s the successful POST single beep code after pressing the start button, and then the black screen. Cannot boot into Windows or BIOS.

Trouble shooting: Removed hard disc & gpu; changed rams & slots; Shorted CMOS jumper for 10 seconds while the PC was turned off; Removed the CMOS battery for few minutes. Didn’t work.

Mainboard: Gigabyte GA Z87 HD3

Background story in brief:
Once I cleaned the board with contact cleaner, and then there was electric burning smell coming from the PC. Confirmed that it wasn’t the PSU. It was the mainboard and the smell was strongest around the onboard Intel chip. However, windows and BIOS booting was working alright for months until, attempted another OS (**ckintosh) installation following video instruction, which required settings changes in BIOS, settings never needed before for windows installation. The installation failed. Rebooted back to windows (without a fresh windows installation), and it did boot to windows few times, but stopped booting into BIOS, and eventually stopped booting into windows. Now just the ‘Black screen with blinking cursor’.

Considering BIOS update using updated BIOS file from manufacturer and the m_BIOS Pins 1 and 6 shorting method. Though, online found, “If you cannot boot into the BIOS or Windows, you most likely will not be able to update your BIOS.” The board has a b_BIOS chip, and in Gigabyte manual it says, backup BIOS should be activated on the next boot, if the main BIOS is corrupted.

Is there a way to fix the board other than replacing the BIOS chip?