Actually, none of those things are likely since it DOES run, and most likely DOES POST, and there is simply nothing on the screen. If it wasn't able to POST it would either loop continuously trying to POST, which you'd be able to determine by the behavior of the lights, fans, beeps, etc. or would shut down. Since it isn't doing those things from what I am understanding and simply doesn't display to the screen, then none of those things is "likely" even if one of them is possible.
And since I already indicated the probability of it being a graphics card issue by asking about it, I would certainly agree that there is a good chance this is the issue and would recommend trying ANY other graphics card. Even a super low end card would be fine or you could certainly find a used Ryzen that has onboard graphics like the 5600G and try that with no graphics card installed at all. Or simply go with a new 4600G or 5600G, something along those lines, that eliminates the possibility that it's a CPU issue, eliminates the possibility that it's a graphics card issue AND gives you a decent bump in CPU performance over your 3600. Just a thought. Certainly a cheap graphics card if you can't borrow one somewhere is the least costly option but then again if it isn't the problem then it's 50-75 bucks you could have put towards a 110-135 dollar Ryzen CPU with onboard graphics that would have had some additional benefits.
Additionally, since it's an NAS box and the graphics aren't terribly important the onboard Radeon graphics should be more than capable enough for the needs of the device.
Just a thought. Eliminating the graphics card though is probably the primary consideration.