First to get your Integrated Graphics to work with the GPU card installed you must go into BIOS and set the Integrated Graphics as your Main Display Device by changing in BIOS settings from "Auto" or "PCIe" to IGP or something like that.
When you have a GPU card installed and BIOS is set for "Auto" it will automatically set your GPU Card as the Main Display device. But once you remove the GPU Card it automatically then switches to your Integrated Graphics.
Once you set in BIOS for the Integrated Graphics as your Main Display Device it should disable the GPU card when installed. Then hopefully you might be able to flash the BIOS on it.
Also if the GPU card is used, you might want to check to make sure it isn't a fake.
EDIT: Here is how to flash your GPU card when it won't POST or go into BIOS from TechPowerUp: https://www.techpowerup.com/forums/threads/how-to-recover-from-a-bad-video-bios-flash.265939/
"Cannot POST/BOOT
There are several methods to deal with a graphics card that is unable to POST and giving a black screen when system is powered on.
1. If your card has dual BIOS, just press the BIOS switch.
2. Use the integrated graphics (onboard graphics) if available. Just plug to the monitor to the motherboard's I/O.
***If you get an add-in graphics card error message, just enable "Intel Multi-Display / iGPU Multi-Monitor" from the motherboard's BIOS***
3. Get an old PCI graphics card.
4. Another PCIe graphics card and motherboard with TWO x16 PCI express slots.
5. SPI flash programmer like FlashcatUSB or CH341A.
Still cannot POST!!!
Even after you used one of the methods above and still cannot POST, your bricked card is probably preventing the system from working. In this case, you'll have to locate the video BIOS chip and short 1-5 pins with a paperclip, or small wire, or by soldering until flashing is complete. The BIOS chip is usually 8-pin and located on the rear, bottom side, tagged as U1-12 on the PCB, but be sure to verify first by searching online the text written on the chip (e.g. A25L0100). Search engine results should be related to "flash memory chip", not a regulator or anything else.