I still think I need to paraphrase some for troubleshooting. Your desired monitors, from GTX 1080 are DisplayPort and HDMI (board) to DVI (monitor). Is there a reason you are using that HDMI connector instead of DVI (from board) to DVI (monitor) which should be more straightforward? The rest of your symptoms remain sounding to me like those NVidia DisplayPort firmware issues supposedly solved by update (that is, not ever seeing BIOS screens on DisplayPort - only seeing them on non-DisplayPort when DisplayPort is disconnected). You first say that both monitors connected end up at Windows desktop, no display before that (my thinking is that it "should" be displaying to DisplayPort so no reason to look for it on the other monitor). If you are trying to get to BIOS with some key like Del then it is still going to try to display on DisplayPort, so it might seem like hang to you. Some other keys would act similar, such as F11 which would be prompting you to select boot device. If I've paraphrased correctly, the part that remains confusing to me is when talk about needing to disconnect DisplayPort monitor then reconnect it and restart to Windows, which seems to contradict what you said about getting to Windows desktop (but not BIOS) with both monitors connected. Are you perhaps describing some difference between "power on" and "restart" style boots?
If my paraphrasing is describing the issue, it might make sense to move this topic to whatever section of the forum covers MSI graphics cards, hoping that someone there might be more familiar and know whether there is indeed some firmware update appropriate. Still need to mention details such as the motherboard since it is presumably related to UEFI.
Note: you might want to name your DVI monitor model in case it has some issue with available resolutions that BIOS might be trying to use, but my guess at this time is that is not part of the problem you are describing (since you can see fine with just that single monitor).
