This sounds exactly like the problem I ran into when I switched to Linux last year. With the exception of Linux Mint, the exact thing happened to my setup on various distros.
tl;dr: For me the issue was/is AMDGPU driver not managing the power state change for my MSI R9 390 correctly.
The PC would randomly lockup in the same way, the screen goes black, keyboard and mouse input drop (my keyboard LEDs turn off, the monitor also goes into standby as if the cable has been removed), the PC remains on but is completely unresponsive (I’ve also noted that the GPU fans spin up)
After a lot of trail and error I found out that it’s to do with incorrect handling of the power states for my MSI R9 390. As far as I can tell once you start doing anything that causes the GPU to change power state (playing video, even opening a web browsers, or in my tests just moving the System Monitor windows quickly back and forth on the desktop) the AMDGPU driver falls over and drops the card.
I’ve tested the R9 390 on two different PCs (Intel i7-4770K MSI Z97 and Intel i7-6850K ASUS x99) with various different distros and experienced the same problem on both machines on all but Linux Mint (I think it was Linux Mint I found to work but it was over a year ago)
I found that when I booted into text mode both machines were perfectly stable. When running in a graphical desktop environment I was able to SSH to the test machine to monitor DMESG and could see the AMDGPU power state change error just before the lockup.
I did a lot of research to try to find a solution. Someone suggested disabling AMDGPU auto power state management (setting kernel param “amdgpu.dpm=0”) but I could not get this to work and as far as I know it means that you need to run the card in “performance” power state all the time or manage the states manually. There’s some info on this here
Unfortunately I was unable to solve the issue, so my R9 390 has been sitting in a box for the past year. The i7-4770K has been running perfectly stable using the on-board Intel graphics and I have had to buy an RX 560 for the i7-6850K, both machines are now running Fedora 28 but have been stable through Fedora 26-28.
I was hoping that newer kernels and AMDGPU releases would solve the issue but only this week I gave the R9 390 another go in the i7-4470K machine with Fedora 28 and kernel 4.17 and the issue is still there
Do you have another GPU you could try to see if this is the same issue?
Edit I just saw that you have an Nvidia GT630, I would suggest trying this GPU to see if it’s the R9 390
Shecks