One part that is essential to your computer's operation is your logic board. Unfortunately, there is no simple way to tell that it is not working right. You can't exactly swap it out with a new one like a failing hard drive, or try removing it like a bad stick of RAM. Here are some things to look out for that can tell you something is up with your logic board.
Have you noticed weird issues with your monitor where it is acting funny? Maybe there is a significant delay when the monitor turns on after starting up your computer, or the monitor is dimmed slightly at settings where you know it is brighter. In extreme situations, the monitor may not even light up at all. Some users will notice flickering with the display or refresh rate problems where the monitor seems to be lagging a bit behind your movements. While some of these issues can be attributed to a bad monitor, they can also be due to a bad logic board.
The logic board can also play into your computer's battery if you have a laptop. A common problem that can happen is that the battery is not charging when it is plugged into a power source. You may get enough power to run the computer just fine, but the battery doesn't seem to charge at all when power is connected. You may have to shut the laptop down completely for the battery to get power, and then watch the battery slowly trickle down with how much power is left in it.
Have certain ports of the computer simply stopped working? You could have a USB port that is dead or is acting much slower than the port next to it. There could be a headphone jack that is not outputting sound, or the sound is crackling and inaudible. A fault logic board doesn't necessarily mean that all of the ports have to stop working, since something could be wrong that is affecting one or two of them.
The logic board is also going to control the fans that cool down your computer. Pay attention to the fans, because you may not hear them kicking on anymore to cool down your computer during processor-intensive tasks. If the computer gets too hot, that can also cause more damage to the logic board as a result.
Noticing these problems? Take your computer into a computer repair shop to get a diagnostic test run on it, and determine exactly what is wrong with your machine.