I've seen this reported before and if it was my PC, ANY BIOS flashing I did would be on a basic system with all unnecessary cards removed. As you have onboard graphics and that's working fine, I suggest you try shutting down the PC and unplugging it from the mains. Then remove the graphics card altogether then boot up using just the onboard graphics and have another go at flashing the BIOS again. Once you have that working fine then shut down, power off and plug the graphics card back in and have another go at getting that to work. You may need to reinstall the graphics card drivers though.
Be aware that in future, it'd be worth removing your graphics card and just using onboard graphics every time when flashing the BIOS.