I am not sure BIOS will work well for installation off this live, as the installation would then convert the hard drive from UEFI to BIOS and might lose all data or something?
Moreover, if 800x600 boots, I do not at all think that this is an UEFI issue.
I think there is a graphics driver issue. To start with, can you look into the BIOS setup settings for graphics? There should be ways for enabling/disabling "discrete" (NVidia) graphics, try all options for that, one of them might lead to a successful boot.