Well, it seem to be my fault.
Meet my culprit:
A cheap 4 USB Port PCI-E card that never did work properly (at least not under Linux), and I used as a somewhat awkward power bank. It seems that this card generated some electrical interference that caused my graphical issues.
The thing that through me off, was the fact that with the nomodset kernel parameter I had no graphics artifacts, so I figured this was a driver issue and not a hardware issue.
Since I gave up on my integrated graphics, I asked for a recommendation of a cheap discrete graphic card, and @Ethanol suggestion a used RX 550 GPU which I was able to find.
Installing it, however was an ordeal. It refused to work properly. I thought that I got a bad unit, but as a last resort (which I should have probably needed to do as my first step) I decided to try and disconnect all unneeded peripherals. Once I disconnected the offending USB card things started to just work.
Now I am happy using my newly purchased card. although I can just as well can use the integrated graphics.
Thank you all for your thoughtful suggestions.
This issue is now resolved.