Describing what is broken:
The computer in question broke a couple weeks ago. Specifically the computer was broken in such a way that when I turn the computer on the computer turns on but the screen does not get any signal!
One thing that might be important to note: The USB keyboard and USB mouse were not lighting up at all (as in the keyboard scrolllock did not light up even when you pressed it. and the mouse optical laser did not turn red).
Not having any screen from the computer is very alarming because without a screen... you are very limited in what you can do to debug the computer.
What changed to cause the broken state:
I have only been using it for internet the last couple of weeks before the computer broke.
The computer started working... but I don't know why:
Today I took out the video card. Then used compressed air to clean the CPU heatsink/fan, the GPU heatsink/fan, clean some dust. (Dust was definitely accumulated but not completely obstructing airflow. The case is Antec 900 and is very spacious.) Then I moved some power cables. I turned on the computer and I noticed that the mouse got power (previously it had not gotten any power). Then I put the video card back in. Turned on the computer and voila... the computer turned on and the screen worked.
I don't know what fixed this computer! What is the most likely thing that fixed this computer? I will auto-upvote anyone who provides credible links to backup their answer.