Mass effect breaks monitor : no signal

I have to agree with @holger1405 on this being a hardware issue and not something done by ME.  The fact that it is now happening with Stardew Valley means it is something other than the running game, as more than one game is having issues.

My personal experience with this kind of thing was a HDMI cable being 60-80% plugged in, ie it was just barely not all the way in and when I plugged it back all the way, issue fixed.  I have zero clue how it got unplugged on the back of my computer, as the computer just sits there unmoving, but it had.  I could also see a port issue on your graphics card being an issue, but there is almost zero chance that Mass Effect did anything to cause this.  At most a game usually shows up a fault in the hardware and not causes said fault....I have heard of some saying a new game killed their machines and maybe on one it has happened but definitely not a game like MELE, that has been out awhile and most times even those games just stressed a component that wasn't in good health to start with.