Russell.... I feel your pain. I have been fighting this problem for 6 weeks with no tangible success. Only occasionally do I get into Windows normally.
After weeks of reading online, I have come across myriad solutions that others claim work for them but have not worked for me. Try some of these:
1. Boot into safe Mode. Go to Device Manager. Go to your display adapter. Uninstall the drives for your video card. Reboot. Reinstall your video drivers. Reboot. Does it work?
2. Go into BIOS. What is your computer's boot preference for video? Is it defaulting to your onboard video instead of your GPU? Or, in your case, the other way around? Does it think your GPU is the default even if your GPU is dead?
3. Can you sleep your computer with a keyboard key when you get the black screen? If so, try waking it up from there.
4. When you get the black screen, unplug your monitor cable from your PC. Plug it back in. If that doesn't work, try blind-typing your password (or just hit enter if you have no password) and getting to desktop blindly. Now unplug the monitor cable and plug it back in. Does it work?
I have a whole list of sites saved on my laptop with many more possible solutions. None of them work. I managed to get into my desktop after 70 minutes of waiting and fooling around with things in my BIOS, but I am sure that when I try to start up again tomorrow I'll get the same black screen...
It is frustrating as heck. I have absolutely no explanation for this nightmare.