Ok I found some free time and continued the investigation. It looks like that the entry for the VBIOS version that applications are taking is in the registry, however I can't determine from where the value is taken. I've made a screenshot showcasing that in registry, DDU and NVIDIA Inspector we have VBIOS ID 80.04.33.00.37 which is not the correct one. I tried to manually edit this for testing purposes - it doesn't matter - this is cached somewhere and programs are not reflecting my change. After a reboot the value is switched back. I have tried to download the 8770w BIOS itself F70 and tried to find inside with HEX editor if we will have the GPU BIOS integrated/as someone suggested in this thread/ - I can;t find any entries for NVIDIA or any vbios ID. Also I don't think it makes a lot of sense - these machines were sold with ~10 different cards and that would mean that the bios will have to contain all of them -> extremely inefficient ~2 megs of rom space!
The true hardware VBIOS ID is 80.04.60.00.33 - I verified this from NVflash tool, also checked the rom files with the HEX editor and the value is matching. I'm missing something here. Are the drivers somehow forcing the OS to think the ID is different and using cached version of the vbios? I tried several restarts, laptop BIOS defaults and whatnot. I really suspect that the drivers are screwing the things up. @Klem I see that you helped a lot of people here - are you able to assist me or point me in the right direction? If I become eligible to download the archive with the files - I see there is one rom for K4000m 80.04.33.00.34 do you think it would be safe to flash? Maybe I could edit the version to match my hardware using the HEX editor, or perhaps this will throw an error as there might be chcksum somewhere?
I'm out of ideas for the moment and I see there is lots of potential for this card.