Hello my friend! I know this question was filed some months ago, but since I think I've found the answer I will still reply it because many other people could have a similar problem.
Well, just like you, I wanted to connect a (secondary) monitor via DVI and my system would just not recognise it! Before windows loaded it would perfectly display the MSI BIOS loading screen and it would also work in safe mode (Windows 10 standard display drivers). At first I thought it could be a dead/faulty DVI port on my GPU, but after trying (like I stated earlier) using it in safe mode, I was sure the port was just fine! After that I thought it would be a driver issue and I reported my problem to AMD several times. I was desperate because I had just spent 300 € on this card (RX480 Sapphire Nitro+ OC) and I was thinking I had made a mistake upgrading because the secondary screen was working just fine with my old GPU (R9 270X Sapphire). Then, I bought a new monitor which was connected via Display Port and it worked just fine. I used my main (HMDI connencted) as secondary and I could finally work on my projects much easier. About 2 months after buying the new monitor, I found a very old 4:3 HP monitor (HP 1755) and thought I should give one more shot to my DVI port. Guess what! It worked! So, it was my old secondary screen that had the problem. But what was it?
Well, I am not a cable/signal expert, but I think the issue is related to RX480 only delivering Digital and not Analog signal. This is why some RX480 models don't even have a DVI port! Both Sapphire (mine) and ASUS (yours) have a DVI-D port, which as far as I know, delivers a digital signal. So the problem should be that your monitor cannot support Digital signal. The HP monitor I tested might be old but was really good when it first came our, so I guess it could support both Digital and Analog signal.
ASUS is a very trusted manufacturer as far as it comes to GPUs and your card should be just fine! I was between the ASUS and Sapphire model (because ASUS can deliver up to 8K while Sapphire can only deliver up to 4K) but I chose the Sapphire model because I have been VERY SATISFIED by what I've got all these years. Still, do not blame your GPU, blame your monitor. Ask for a friend for a DVI monitor and try it. If it works, then that's it! My DVI monitor was from a "local" (shipped from China) brand and was kinda crap. You simply cannot compare it to a HP monitor, despite it being MANY years old!
I really hope I helped! I need to state that I am not sure about what I said about the Digital and Analog signal, as I am not an expert.