How many different ways for a laptop to die, and with what signs?
There are many possibilities.
Dies instantly: could happen - shuts down suddenly, and no recovery possible. This would be unusual, but could be loss of battery, plus failure of the power supply on the logic board. You are working, and it suddenly freezes, never to return.
Loss of battery, cable on power adapter fails because of an overheat, etc.
Slow indicators of failure, such as:
loss of backlight on display, video flashing, vertical or horizontal lines on the screen, pixel failures on the LCD panel.
Loss of sound, or speaker gets very distorted/buzzes.
Noise/clicking from the hard drive.
Keyboard keys fail, or whole sections of keyboard quit responding.
Trackpad stops working, or is very intermittent
Battery swells, causing a variety of mechanical issues, maybe ruining the trackpad or the upper case/keyboard
System takes very long time to boot, or shows intermittent error messages during boot, or just does not function like it has in the past.
CD/DVD drive stops reading disks, or very intermittent, or noisy when operating.
System is completely quiet, because one or both fans stop working.
etc. / etc. / ad infinitum
Working in a service shop, I have seen many kinds of failures.
Some of these can take a long time (several months) to make the system fail, or others might happen in seconds - literally in the blink of an eye, like a catastrophic failure of a hard drive (where you hear parts come loose

)
What do you look for? Unusual noises. Overheating/temps much higher than normal. Unusual smells.
Flashing sparks or actual flames, with or without smoke, would be exciting, I think,

and might lead me to suspect that something has failed...