I have quite a similar problem with HP ProBook 470 G0
It has a ATI HD 8750M, but when i updated to WIndows 8.1 (64Bit) i got the black screen/blinks on boot.
I found a BIOS option calles "Changable GRaphics" or something like that. After disabling this option th Laptop boots just fine, but the ATI Card wont be shown in the Device Manager at all and i can not install any driver.
I really need that graphic card, so is there any way to solve this? or can i just reinstall windows 8 and live with it?