Okay, so I made the decision to get a new monitor for my desktop, instead of all the ideas of running my Desktop Linux pc through a separate laptop. When I hook it up and turn on the desktop power, it runs for maybe 3 or 4 seconds, then kicks off. And same thing again, and again. It did that last time I had it up and running, and it straightened out but I can't remember what I did to get it working last time.
As I read your post, it appears you had the monitor running ... "straightened out" ... but it's just that you have forgotten what you did to get it working. If that's correct, then, as you say, you have to do what you did. First you need to make sure the hardware is all connected up soundly as mentioned.
These thoughts come to mind.
Reset the monitor itself to "Factory settings". You need to go into the monitor's own controls to find where you need to choose this option. It's usually under "Management" or something similar. "Factory settings" pretty much assures you that the monitor is in the best condition to work because manufactures usually set the monitors to work out of the box.
What happens if you load a live usb? If that runs on screen, then you may be looking at needing to choose some driver options or firmware for your installed system, but that would be a good outcome and dispel the hardware theory.
If the live usb runs, then it would be helpful if you record the output to:
lspci -nnk |grep -A3 -i vga