Onboard graphics - not all CPUs have on-chip GPU, highest tier, high performance CPUs don't have integrated GPUs.
PCIe GPUs are very sensitive to power supply quality, get errors and even totally fails from unstable power.
Best option would be insert some simple cheap GPU in PCIe slot and try to enter to BIOS, but in Windows 10 and quick boot option active it's near impossible enter BIOS menu by F2/F10/Del (depends on motherboard brand). In this case clearing BIOS options by jumper will be necessary, after that BIOS will start on first available graphic port. Monitor and signal cable should be connected before powering PC for proper detection video output.
Source of this problem, (assuming cables and monitors are confirmed good) may be:
1. Bad/worn power supply.
2. Overheated and broken GPU. Don't test it in other essential system because of high chance to smoke other motherboard.
3. Dirty/corroded PCIe slot.
BIOS seems good (one beep after power on selftest), same for RAM and CPU - core hardware seems work fine.